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 A091056 #21 Feb 16 2025 08:32:52
%S A091056 0,0,1,5,33,193,1169,6993,42001,251921,1511697,9069841,54419729,
%T A091056 326517009,1959104785,11754623249,70527750417,423166480657,
%U A091056 2538998927633,15233993478417,91403961045265,548423765922065
%N A091056 Expansion of x^2/((1-x)*(1+2*x)*(1-6*x)).
%C A091056 4*A091055(n) counts walks of length n between non-adjacent vertices of the Johnson graph J(5,2).
%C A091056 6^n = A091054(n) + 6*A091055(n) + 12*a(n).
%H A091056 G. C. Greubel, <a href="/A091056/b091056.txt">Table of n, a(n) for n = 0..1000</a>
%H A091056 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>
%H A091056 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,8,-12).
%F A091056 a(n) = (3 * 6^n + 5*(-2)^n - 8)/120.
%F A091056 a(0)=0, a(1)=0, a(2)=1, a(n) = 5*a(n-1) + 8*a(n-2) - 12*a(n-3). - _Harvey P. Dale_, Apr 02 2015
%F A091056 E.g.f.: (3*exp(6*x) + 5*exp(-2*x) - 8*exp(x))/120. - _G. C. Greubel_, Dec 27 2019
%p A091056 seq( (3*6^n +5*(-2)^n -8)/120, n=0..40); # _G. C. Greubel_, Dec 27 2019
%t A091056 CoefficientList[Series[x^2/((1-x)(1+2x)(1-6x)),{x,0,40}],x] (* or *) LinearRecurrence[{5,8,-12},{0,0,1},40] (* _Harvey P. Dale_, Apr 02 2015 *)
%o A091056 (PARI) vector(41, n, (3*6^(n-1) + 5*(-2)^(n-1) - 8)/120) \\ _G. C. Greubel_, Dec 27 2019
%o A091056 (Magma) [(3*6^n +5*(-2)^n -8)/120: n in [0..40]]; // _G. C. Greubel_, Dec 27 2019
%o A091056 (Sage) [(3*6^n +5*(-2)^n -8)/120 for n in (0..40)] # _G. C. Greubel_, Dec 27 2019
%o A091056 (GAP) List([0..40], n-> (3*6^n +5*(-2)^n -8)/120); # _G. C. Greubel_, Dec 27 2019
%Y A091056 Cf. A091054, A091055.
%K A091056 easy,nonn
%O A091056 0,4
%A A091056 _Paul Barry_, Dec 17 2003