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List of nonzero determinants of Unbordered Lights Out matrices UBL_k.
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%I #16 May 13 2020 07:04:40

%S 80,-1215,142805,-7004233215,870763219280,87789257318405,

%T 45421053339522658203125,-7059547871395329316834815,

%U -19913109703689000789427796194815,42950557989828549673287680,940419421873808776346210289268985127605

%N List of nonzero determinants of Unbordered Lights Out matrices UBL_k.

%C For the orders of these matrices see A296352.

%H Amiram Eldar, <a href="/A296353/b296353.txt">Table of n, a(n) for n = 1..31</a>

%H Martin Kreh, <a href="https://doi.org/10.4169/amer.math.monthly.124.10.937">"Lights Out" and Variants</a>, Amer. Math. Month., Vol. 124 (10), Dec. 2017, pp. 937-950.

%t 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 *)

%Y Cf. A296350, A296351, A296352.

%K sign

%O 1,1

%A _N. J. A. Sloane_, Dec 14 2017