A296352 -id:A296352 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 14 2017

sign

For the orders of these matrices see A296350.

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.

Cf. A296350, A296352, A296353.

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 *)

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Dec 14 2017

sign

For the orders of these matrices see A296352.

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.

Cf. A296350, A296351, A296352.

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 *)

A296350 List of numbers k such that the determinant of the Bordered Lights Out matrix BL_k is nonzero.

Original entry on oeis.org

2, 3, 6, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 33, 36, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 52, 55, 56, 57, 58, 60, 61, 62, 63, 66, 67, 68, 70, 72, 73, 75, 76, 78, 80, 81, 82, 85, 86, 87, 88, 90, 91, 92, 93, 96, 97, 98, 100, 102

Offset: 1

N. J. A. Sloane, Dec 14 2017

nonn

Martin Kreh, "Lights Out" and Variants, Amer. Math. Month., Vol. 124 (10), Dec. 2017, pp. 937-950.

Cf. A296351, A296352, A296353.

Select[Range[2, 102], Mod[# + 1, 5] > 0 && Mod[# + 1, 6] > 0 &] (* Amiram Eldar, May 13 2020 *)

Numbers m > 1 such that m+1 is not divisible by 5 nor by 6. - Amiram Eldar, May 13 2020

More terms from Amiram Eldar, May 13 2020

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

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

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A296350 List of numbers k such that the determinant of the Bordered Lights Out matrix BL_k is nonzero.

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