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 A096980 #26 Sep 08 2019 02:43:05
%S A096980 1,5,17,69,257,997,3793,14565,55681,213317,816401,3126021,11966849,
%T A096980 45815845,175399633,671510181,2570817793,9842206853,37680138257,
%U A096980 144255724485,552272416769,2114334904933,8094576727249,30989497789029
%N A096980 Expansion of (1+3x)/(1-2x-7x^2).
%C A096980 Second binomial transform is A002315 (NSW numbers). Binomial transform of A094015.
%C A096980 Binomial transform is A108051 (shifted left, without leading zero). - _R. J. Mathar_, Jul 11 2012
%H A096980 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,7).
%F A096980 a(n) = (1+sqrt(2))*(1+2*sqrt(2))^n/2 + (1-sqrt(2))*(1-2*sqrt(2))^n/2.
%F A096980 a(n) = 3*Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k)*(7/2)^k*2^(n-k-1) + Sum_{k=0..floor(n/2)} binomial(n-k, k)*(7/2)^k*2^(n-k).
%F A096980 a(n) = A015519(n+1) + 3*A015519(n). - _R. J. Mathar_, Jul 11 2012
%F A096980 Satisfies recurrence relation system a(n) = 3*a(n-1) + 2*b(n-1), b(n) = 2*a(n-1) - b(n-1), a(0)=1, b(0)=1. - _Ilya Gutkovskiy_, Apr 11 2017
%o A096980 (PARI) x='x + O('x^24); Vec((1 + 3*x)/(1 - 2*x - 7*x^2)) \\ _Indranil Ghosh_, Apr 11 2017
%Y A096980 Cf. A002315, A094015, A108051, A015519.
%K A096980 easy,nonn
%O A096980 0,2
%A A096980 _Paul Barry_, Jul 17 2004