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A296353
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List of nonzero determinants of Unbordered Lights Out matrices UBL_k.
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4
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80, -1215, 142805, -7004233215, 870763219280, 87789257318405, 45421053339522658203125, -7059547871395329316834815, -19913109703689000789427796194815, 42950557989828549673287680, 940419421873808776346210289268985127605
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OFFSET
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1,1
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COMMENTS
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For the orders of these matrices see A296352.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..31
Martin Kreh, "Lights Out" and Variants, Amer. Math. Month., Vol. 124 (10), Dec. 2017, pp. 937-950.
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MATHEMATICA
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K[n_] := Table[If[MemberQ[{0, 1, n - 1}, Abs[i - j]], 1, 0], {i, 1, n}, {j, 1, n}]; UL[n_] := KroneckerProduct[(kn = K[n]), (in = IdentityMatrix[n])] + KroneckerProduct[in, kn] - IdentityMatrix[n^2]; Select[Table[Det @ UL[n], {n, 3, 20}], # != 0 &] (* Amiram Eldar, May 13 2020 *)
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CROSSREFS
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Cf. A296350, A296351, A296352.
Sequence in context: A251427 A275701 A168364 * A126861 A038727 A204476
Adjacent sequences: A296350 A296351 A296352 * A296354 A296355 A296356
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane, Dec 14 2017
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STATUS
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approved
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