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 A121963 #20 Sep 08 2022 08:45:27
%S A121963 0,1,2,7,23,53,182,599,1380,4739,15597,35933,123396,406121,935638,
%T A121963 3213035,10574743,24362521,83662306,275349439,634361184,2178432991,
%U A121963 7169660157,16517753305,56722920072,186686513521,430095947114
%N A121963 Expansion of x^2*(1 + 2*x + 7*x^2 - 3*x^3 + x^4)/(1 - 26*x^3 - x^6).
%C A121963 a(n) is a component of the n-th partial product of 2 X 2 matrices with rows (0,1), (1, 1 + A130196(j)), j>=1.
%C A121963 The linear recurrence shows that these are three interleaved sequences (0,7,182,...), (1,23,599,...) and (2,53,1380,...) obeying simple recurrences of the form b(n) = 26*b(n-1) + b(n-2).
%H A121963 G. C. Greubel, <a href="/A121963/b121963.txt">Table of n, a(n) for n = 1..1000</a>
%H A121963 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,26,0,0,1).
%p A121963 seq(coeff(series(x^2*(1+2*x+7*x^2-3*x^3+x^4)/(1-26*x^3-x^6), x, n+1), x, n), n = 1..30); # _G. C. Greubel_, Oct 05 2019
%t A121963 M[n_] := {{0,1}, {1, 1+Mod[n^2-n-1, 3]} }; v[1] = {0,1}; v[n_] := v[n] = M[n].v[n-1]; Table[v[n][[1]], {n,30}]
%t A121963 Rest@CoefficientList[Series[x^2*(1+2*x+7*x^2-3*x^3+x^4)/(1-26*x^3-x^6), {x,0,30}], x] (* _G. C. Greubel_, Oct 05 2019 *)
%o A121963 (PARI) my(x='x+O('x^30)); concat([0], Vec(x^2*(1+2*x+7*x^2-3*x^3 +x^4)/( 1-26*x^3-x^6))) \\ _G. C. Greubel_, Oct 05 2019
%o A121963 (Magma) I:=[0,1,2,7,23,53]; [n le 6 select I[n] else 26*Self(n-3) +Self(n-6): n in [1..30]]; // _G. C. Greubel_, Oct 05 2019
%o A121963 (Sage)
%o A121963 def A121963_list(prec):
%o A121963 P.<x> = PowerSeriesRing(ZZ, prec)
%o A121963 return P( x^2*(1+2*x+7*x^2-3*x^3+x^4)/(1-26*x^3-x^6) ).list()
%o A121963 a=A121963_list(30); a[1:] # _G. C. Greubel_, Oct 05 2019
%o A121963 (GAP) a:=[1,2,9];; for n in [7..30] do a[n]:=26*a[n-3]+a[n-6]; od; a; # _G. C. Greubel_, Oct 05 2019
%K A121963 nonn,easy
%O A121963 1,3
%A A121963 _Roger L. Bagula_, Sep 02 2006