A296353 List of nonzero determinants of Unbordered Lights Out matrices UBL_k.

80, -1215, 142805, -7004233215, 870763219280, 87789257318405, 45421053339522658203125, -7059547871395329316834815, -19913109703689000789427796194815, 42950557989828549673287680, 940419421873808776346210289268985127605

Offset: 1

Author

N. J. A. Sloane, Dec 14 2017

Keywords

• sign

Comments

For the orders of these matrices see A296352.

Links

• 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.

Crossrefs

Cf. A296350, A296351, A296352.

Programs

Mathematica

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 *)