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A192892 Number of n X n binary matrices whose determinants equal their permanents.

%I A192892 #36 Oct 01 2021 13:17:19
%S A192892 1,2,12,343,34997,12515441,15749457081,72424550598849,
%T A192892 1282759836215548737
%N A192892 Number of n X n binary matrices whose determinants equal their permanents.
%C A192892 Lower bounded by A088672.
%C A192892 Similar to A145675 and A145676.
%H A192892 Christopher Culter, <a href="https://github.com/Culter/PermDet">C++ code to compute large terms</a>
%H A192892 Math StackExchange, <a href="http://math.stackexchange.com/q/1707432/87023">What is the number of n X n binary matrices A such that det(A)=perm(A)?</a>
%F A192892 a(n) <= 2^(n^2), with equality for n<=1.
%e A192892 a(2) equals 12 because there are exactly twelve 2 X 2 binary matrices whose determinants equal their permanents; these matrices are:
%e A192892 |0 0|  |1 0|  |0 1|  |1 1|  |0 0|  |1 0|  |0 0|  |1 0|
%e A192892 |0 0|  |0 0|  |0 0|  |0 0|  |1 0|  |1 0|  |0 1|  |0 1|
%e A192892 .
%e A192892 |0 1|  |1 1|  |0 0|  |1 0|
%e A192892 |0 1|  |0 1|  |1 1|  |1 1|
%t A192892 Sum[KroneckerDelta[Det[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]], Permanent[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]]], {k, 0, (2^(n^2)) - 1}]
%o A192892 (Python)
%o A192892 from itertools import product
%o A192892 from sympy import Matrix
%o A192892 def A192892(n): return 1 if n == 0 else sum(1 for m in product([0,1],repeat=n**2) if (lambda x:x.det()==x.per())(Matrix(n,n,m))) # _Chai Wah Wu_, Oct 01 2021
%Y A192892 Cf. A046747, A087983, A089472, A089477, A145675, A145676.
%K A192892 hard,more,nonn,nice
%O A192892 0,2
%A A192892 _John M. Campbell_, Jul 11 2011
%E A192892 a(0)=1 prepended and a(5)-a(8) from _Christopher Culter_, Apr 13 2016
%E A192892 Definition and example slightly modified by _Harvey P. Dale_, Feb 24 2017