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 A098523 #10 Jul 07 2023 08:33:24
%S A098523 1,1,2,2,2,3,4,6,8,10,13,17,23,31,41,54,71,94,125,166,220,291,385,510,
%T A098523 676,896,1187,1572,2082,2758,3654,4841,6413,8495,11253,14907,19748,
%U A098523 26161,34656,45909,60816,80564,106725,141381,187290,248106
%N A098523 Expansion of (1+x^2)/(1-x-x^5) = (1+x^2)/((1-x+x^2)*(1-x^2-x^3)).
%C A098523 The expansion of (1+kx^2)/(1-x-k^2*x^5) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-5),a(0)=1,a(1)=1,a(2)=k+1,a(3)=k+1,a(4)=k+1, with a(n)=sum{k=0..floor(n/2), binomial(n-2k,floor(k/2))r^k}.
%H A098523 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1).
%F A098523 a(n)=a(n-1)+a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))}.
%F A098523 7*a(n) = 8*A182097(n) +5*A182097(n-1) +3*A182097(n-2) - A010892(n) +3*A010892(n-1). - _R. J. Mathar_, Jul 07 2023
%t A098523 CoefficientList[Series[(1+x^2)/(1-x-x^5),{x,0,50}],x] (* or *) LinearRecurrence[ {1,0,0,0,1},{1,1,2,2,2},50] (* _Harvey P. Dale_, Mar 05 2014 *)
%Y A098523 Cf. A097333.
%K A098523 easy,nonn
%O A098523 0,3
%A A098523 _Paul Barry_, Sep 12 2004