This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A162698 #35 Sep 04 2023 13:48:20
%S A162698 4,5,9,11,14,17,19,23,24,29,34,35,39,41,44,47,49,53,54,59,64,65,69,71,
%T A162698 74,77,79,83,84,89,94,95,99,101,104,107,109,113,114,119,124,125,129,
%U A162698 131,134,137,139,143,144,149,154,155,159,161,164,167,169,173,174,179,184,185,189,191,194,197,199
%N A162698 Numbers n such that the incidence matrix of the grid n X n has -1 as eigenvalue.
%C A162698 Numbers n such that n+1 is a multiple of 5 or 6. - _Tom Edgar_, Dec 15 2017
%H A162698 Colin Barker, <a href="/A162698/b162698.txt">Table of n, a(n) for n = 1..1000</a>
%H A162698 M. 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.
%H A162698 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-2,2,-2,2,-1).
%F A162698 G.f.: x*(x^9+4*x^8-3*x^7+7*x^6-5*x^5+8*x^4-5*x^3+7*x^2-3*x+4) / ((x-1)^2*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Dec 03 2012 ["Empirical" removed after Tom Edgar's comment by _Andrey Zabolotskiy_, Dec 15 2017]
%F A162698 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-10) for n>10.
%t A162698 With[{nn=40},Select[Union[Join[5*Range[nn],6*Range[nn]]]-1,#<=5nn&]] (* _Harvey P. Dale_, Sep 04 2023 *)
%o A162698 (PARI) for(n=1,100, if( matdet(matrix(n^2,n^2,i,j, (abs((i-1)\n - (j-1)\n) + abs((i-1)%n - (j-1)%n)==1) + (i==j) ))==0, print1(n,", ") ) ) \\ _Max Alekseyev_, Apr 23 2010
%o A162698 (PARI) Vec(x*(x^9+4*x^8-3*x^7+7*x^6-5*x^5+8*x^4-5*x^3+7*x^2-3*x+4) / ((x-1)^2*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Dec 15 2017
%o A162698 (Sage) [n for n in [1..200] if (n+1)%5==0 or (n+1)%6==0] # _Tom Edgar_, Dec 15 2017
%Y A162698 Cf. A093509, A117870.
%K A162698 nonn,easy
%O A162698 1,1
%A A162698 _Vincent Delecroix_, Jul 11 2009
%E A162698 Twelve more terms from _Max Alekseyev_, Apr 23 2010
%E A162698 a(33)-a(40) from _Max Alekseyev_, Feb 15 2013
%E A162698 More terms from _Tom Edgar_, Dec 15 2017