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A192892 Number of n X n binary matrices whose determinants equals 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

Table of n, a(n) for n=0..8.

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 August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)