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 A095310 #17 Aug 29 2024 00:56:20
%S A095310 1,5,12,38,107,316,915,2671,7771,22640,65922,191993,559112,1628281,
%T A095310 4741905,13809541,40216516,117119750,341079507,993301748,2892722267,
%U A095310 8424270271,24533405595,71446899736,208069745986,605946785585
%N A095310 a(n+3) = 2*a(n+2) + 3*(n+1) - a(n).
%C A095310 Let M = the 3 X 3 matrix [1 1 1 / 3 1 0 / 1 0 0], then M^n * [1 0 0] = [a(n) q a(n-1)] where q is another sequence with the same recursion rule.
%H A095310 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, -1).
%F A095310 G.f.: (-x^2+3*x+1)/(x^3-3*x^2-2*x+1). - _Harvey P. Dale_, Jan 25 2014
%e A095310 a(6) = 316 = 2*107 + 3*38 - 12.
%e A095310 a(5) = 107 since M^5 * [1 0 0] = [107 q 38].
%t A095310 a[n_] := (MatrixPower[{{1, 1, 1}, {3, 1, 0}, {1, 0, 0}}, n].{{1}, {0}, {0}})[[1, 1]]; Table[ a[n], {n, 27}] (* _Robert G. Wilson v_, Jun 05 2004 *)
%t A095310 LinearRecurrence[{2,3,-1},{1,5,12},30] (* _Harvey P. Dale_, Jan 25 2014 *)
%Y A095310 Cf. A001263, A006356, A006054, A061646, A061647, A095125, A095126.
%K A095310 nonn,easy
%O A095310 1,2
%A A095310 _Gary W. Adamson_, Jun 02 2004
%E A095310 Corrected and extended by _Robert G. Wilson v_, Jun 05 2004
%E A095310 Edited by _N. J. A. Sloane_, Jun 07 2004