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 A192892 Number of n X n binary matrices whose determinants equal their permanents. 0
 1, 2, 12, 343, 34997, 12515441, 15749457081, 72424550598849, 1282759836215548737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Lower bounded by A088672. Similar to A145675 and A145676. LINKS Christopher Culter, C++ code to compute large terms Math StackExchange, What is the number of n X n binary matrices A such that det(A)=perm(A)? FORMULA a(n) <= 2^(n^2), with equality for n<=1. EXAMPLE a(2) equals 12 because there are exactly twelve 2 X 2 binary matrices whose determinants equal their permanents; these matrices are: |0 0|  |1 0|  |0 1|  |1 1|  |0 0|  |1 0|  |0 0|  |1 0| |0 0|  |0 0|  |0 0|  |0 0|  |1 0|  |1 0|  |0 1|  |0 1| . |0 1|  |1 1|  |0 0|  |1 0| |0 1|  |0 1|  |1 1|  |1 1| MATHEMATICA 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}] CROSSREFS Cf. A046747, A087983, A089472, A089477, A145675, A145676. Sequence in context: A088229 A060596 A074257 * A105231 A009398 A009698 Adjacent sequences:  A192889 A192890 A192891 * A192893 A192894 A192895 KEYWORD hard,more,nonn,nice AUTHOR John M. Campbell, Jul 11 2011 EXTENSIONS a(0)=1 prepended and a(5)-a(8) from Christopher Culter, Apr 13 2016 Definition and example slightly modified by Harvey P. Dale, Feb 24 2017 STATUS approved

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Last modified June 21 00:06 EDT 2021. Contains 345319 sequences. (Running on oeis4.)