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 A099098 #20 May 29 2025 16:33:48
%S A099098 1,1,4,12,37,114,351,1081,3329,10252,31572,97229,299426,922111,
%T A099098 2839729,8745217,26931732,82938844,255418101,786584466,2422362079,
%U A099098 7459895657,22973462017,70748973084,217878227876,670976837021,2066337330754
%N A099098 Quadrisection of a Padovan sequence.
%C A099098 Quadrisection of sequence with g.f. 1/(1-x^2-x^3), or A000931(n+3).
%H A099098 Harvey P. Dale, <a href="/A099098/b099098.txt">Table of n, a(n) for n = 0..1000</a>
%H A099098 Sela Fried, <a href="https://arxiv.org/abs/2505.14196">Even-up words and their variants</a>, arXiv:2505.14196 [math.CO], 2025. See p. 4.
%H A099098 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,1).
%F A099098 G.f.: (1-x-x^2)/(1-2x-3x^2-x^3);
%F A099098 a(n)=sum{k=0..2n, binomial(k, 4n-2k)};
%F A099098 a(n)=2a(n-1)+3a(n-2)+a(n-3);
%F A099098 a(n)=A000931(4n+3).
%F A099098 a(n) = Sum [k=0..n, C(2n-k, 2k) ].
%e A099098 1 + x + 4*x^2 + 12*x^3 + 37*x^4 + 114*x^5 + 351*x^6 + ...
%t A099098 LinearRecurrence[{2,3,1},{1,1,4},40] (* _Harvey P. Dale_, Aug 23 2011 *)
%Y A099098 Bisection of A005251.
%K A099098 easy,nonn
%O A099098 0,3
%A A099098 _Paul Barry_, Sep 29 2004