A296351 List of nonzero determinants of Bordered Lights Out matrices BL_k.

-3, -7, 2197, -34391, -4002939, 276762749, -133968364171875, -239121867667810023, 105499562776343659717577, -3916466797684156666150912, -684705401333128471131344184438251, 225821697750350580274314863789803277056101, -2768960885387220187221550050659464666284508951

Offset: 1

Author

N. J. A. Sloane, Dec 14 2017

Keywords

• sign

Comments

For the orders of these matrices see A296350.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..37
• Martin Kreh, "Lights Out" and Variants, Amer. Math. Month., Vol. 124 (10), Dec. 2017, pp. 937-950.

Crossrefs

Cf. A296350, A296352, A296353.

Programs

Mathematica

J[n_] := Table[If[Abs[i - j] < 2, 1, 0], {i, 1, n}, {j, 1, n}]; BL[n_] := KroneckerProduct[(jn = J[n]), (in = IdentityMatrix[n])] + KroneckerProduct[in, jn] - IdentityMatrix[n^2]; Select[Table[Det @ BL[n], {n, 2, 21}], # != 0 &] (* Amiram Eldar, May 13 2020 *)