Testing various optional and external packages (on June 15, but I am 
reporting only now sorry for the delay), I get

Using 
--optional=4ti2,cbc,ccache,cryptominisat,dot2tex,e_antic,external,fricas,glucose,latte_int,lidia,lrslib,memlimit,normaliz,notedown,openssl,pandoc_attributes,pycosat,pynormaliz,rst2ipynb,sage,sage_numerical_backends_coin,sage_numerical_backends_cplex,sage_numerical_backends_gurobi

----------------------------------------------------------------------
sage -t --long src/sage/combinat/matrices/hadamard_matrix.py  # 1 doctest 
failed
sage -t --long src/sage/combinat/quickref.py  # 1 doctest failed
sage -t --long src/sage/combinat/species/library.py  # 1 doctest failed
sage -t --long src/sage/combinat/tutorial.py  # 1 doctest failed
sage -t --long src/sage/databases/findstat.py  # 17 doctests failed
sage -t --long src/sage/databases/oeis.py  # 1 doctest failed
sage -t --long src/sage/geometry/polyhedron/base.py  # Bad exit: 1
sage -t --long src/sage/graphs/generators/smallgraphs.py  # 2 doctests 
failed
sage -t --long src/sage/sat/boolean_polynomials.py  # 1 doctest failed
----------------------------------------------------------------------
External software detected for doctesting: 
cplex,ffmpeg,graphviz,imagemagick,internet,latex,pandoc

Rerunning failed tests, I get

----------------------------------------------------------------------
sage -t --long src/sage/combinat/quickref.py  # 1 doctest failed
sage -t --long src/sage/combinat/species/library.py  # 1 doctest failed
sage -t --long src/sage/combinat/tutorial.py  # 1 doctest failed
sage -t --long src/sage/databases/findstat.py  # 17 doctests failed
sage -t --long src/sage/databases/oeis.py  # 1 doctest failed
sage -t --long src/sage/geometry/polyhedron/base.py  # Bad exit: 1
sage -t --long src/sage/graphs/generators/smallgraphs.py  # 2 doctests 
failed
----------------------------------------------------------------------
External software detected for doctesting: internet


Many of them are related to recent changes in oeis, see below.


sage -t --long src/sage/combinat/quickref.py
**********************************************************************
File "src/sage/combinat/quickref.py", line 9, in sage.combinat.quickref
Failed example:
    s[0].programs() # optional - internet
Expected:
    0: (PARI) {a(n) = if( n<0, 0, n!^2 * 4^n * polcoeff( 1 / besselj(0, x + 
x * O(x^(2*n))), 2*n))}; /* _Michael Somos_, May 17 2004 */
Got:
    [('maple', 0: A000275 := proc(n) sum(z^k/k!^2, k = 0..infinity);
      1: series(%^x, z=0, n+1): n!^2*coeff(%,z,n); add(abs(coeff(%,x,k)), 
k=0..n) end:
      2: seq(A000275(n), n=0..17); # _Peter Luschny_, May 27 2017),
     ('mathematica',
      0: a[0] = 1; a[n_] := a[n] = Sum[(-1)^(r+n+1)*Binomial[n, r]^2 a[r], 
{r, 0, n-1}]; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 05 
2013 *)
      1: CoefficientList[Series[1/BesselJ[0,Sqrt[4*x]], {x, 0, 20}], x]* 
Range[0, 20]!^2 (* _Vaclav Kotesovec_, Mar 02 2014 *)
      2: a[ n_] := If[ n < 0, 0, (n! 2^n)^2 SeriesCoefficient[ 1 / BesselJ[ 
0, x], {x, 0, 2 n}]]; (* _Michael Somos_, Aug 20 2015 *)),
     ('pari',
      0: {a(n) = if( n<0, 0, n!^2 * 4^n * polcoeff( 1 / besselj(0, x + x * 
O(x^(2*n))), 2*n))}; /* _Michael Somos_, May 17 2004 */)]
**********************************************************************
1 item had failures:
   1 of  22 in sage.combinat.quickref
    5 not tested tests not run
    0 tests not run because we ran out of time
    [21 tests, 1 failure, 3.06 s]


sage -t --long src/sage/combinat/species/library.py
**********************************************************************
File "src/sage/combinat/species/library.py", line 104, in 
sage.combinat.species.library.BinaryTreeSpecies
Failed example:
    oeis(seq)[0]                              # optional -- internet
Expected:
    A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = 
(2n)!/(n!(n+1)!). Also called Segner numbers.
Got:
    A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = 
(2n)!/(n!(n+1)!).
**********************************************************************
1 item had failures:
   1 of  10 in sage.combinat.species.library.BinaryTreeSpecies
    0 tests not run because we ran out of time
    [23 tests, 1 failure, 4.48 s]



sage -t --long src/sage/combinat/tutorial.py
**********************************************************************
File "src/sage/combinat/tutorial.py", line 224, in sage.combinat.tutorial
Failed example:
    oeis([1,1,2,5,14])                            # optional -- internet
Expected:
    0: A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = 
(2n)!/(n!(n+1)!). Also called Segner numbers.
    1: ...
    2: ...
Got:
    0: A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = 
(2n)!/(n!(n+1)!).
    1: A022562: Number of connected claw-free unlabeled graphs on n nodes.
    2: A124302: Number of set partitions with at most 3 blocks; number of 
Dyck paths of height at most 4; dimension of space of symmetric polynomials 
in 3 noncommuting variables.
**********************************************************************
1 item had failures:
   1 of 248 in sage.combinat.tutorial
    5 tests for not implemented functionality not run
    6 not tested tests not run
    1 py2 test not run
    0 tests not run because we ran out of time
    [247 tests, 1 failure, 18.41 s]



sage -t --long src/sage/databases/oeis.py
**********************************************************************
File "src/sage/databases/oeis.py", line 492, in 
sage.databases.oeis.OEIS.find_by_description
Failed example:
    oeis('beaver', max_results=4, first_result=2)     # optional -- internet
Expected:
    0: A131956: Busy Beaver variation: maximum number of steps for ...
    1: A141475: Number of Turing machines with n states following ...
    2: A131957: Busy Beaver sigma variation: maximum number of 1's ...
    3: A...: ...
Got:
    0: A131956: Busy Beaver variation: maximum number of steps for a 
2-state, 2-symbol Turing machine running on a tape which is initialized 
with the number n in binary and 0's everywhere else. The machine is started 
at the rightmost bit in the number n.
    1: A141475: Number of Turing machines with n states following the 
standard formalism of the busy beaver problem where the head of a Turing 
machine either moves to the right or to the left, but none once halted.
    2: A333479: Busy Beaver for binary lambda calculus: the maximum normal 
form size of any closed lambda term of size n, or 0 if no closed term of 
size n exists.
    3: A131957: Busy Beaver sigma variation: maximum number of 1's on the 
final tape, for a 2-state, 2-symbol Turing machine running on a tape which 
is initialized with the number n in binary and 0's everywhere else. The 
machine is started at the rightmost bit in the number n.
**********************************************************************
1 item had failures:
   1 of   5 in sage.databases.oeis.OEIS.find_by_description
    5 webbrowser tests not run
    0 tests not run because we ran out of time
    [287 tests, 1 failure, 39.53 s]



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