The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #16 May 13 2020 07:04:26
%S -3,-7,2197,-34391,-4002939,276762749,-133968364171875,
%T -239121867667810023,105499562776343659717577,
%U -3916466797684156666150912,-684705401333128471131344184438251,225821697750350580274314863789803277056101,-2768960885387220187221550050659464666284508951
%N List of nonzero determinants of Bordered Lights Out matrices BL_k.
%C For the orders of these matrices see A296350.
%H Amiram Eldar, <a href="/A296351/b296351.txt">Table of n, a(n) for n = 1..37</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 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 *)
%Y Cf. A296350, A296352, A296353.
%K sign
%O 1,1
%A _N. J. A. Sloane_, Dec 14 2017