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 A361229 #34 Dec 04 2023 06:22:42
%S A361229 1,0,0,0,1,2,3,4,7,14,27,48,84,152,284,532,987,1826,3401,6384,12024,
%T A361229 22656,42728,80780,153151,290970,553601,1054688,2012373,3845646,
%U A361229 7359345,14100692,27048061,51941850,99855389,192163904,370159216,713672568,1377168108,2659729380
%N A361229 G.f. A(x) satisfies A(x) = 1 + x^4 * (A(x) / (1 - x))^2.
%F A361229 G.f.: A(x) = 2*(1-x) / (1-x+sqrt((1-x)^2-4*x^4)).
%F A361229 a(n) = Sum_{k=0..floor(n/4)} binomial(n-2*k-1,n-4*k) * binomial(2*k,k) / (k+1).
%F A361229 D-finite with recurrence (n+4)*a(n) +(-3*n-7)*a(n-1) +(3*n+2)*a(n-2) +(-n+1)*a(n-3) +4*(-n+2)*a(n-4) +4*(n-4)*a(n-5)=0. - _R. J. Mathar_, Dec 04 2023
%p A361229 A361229 := proc(n)
%p A361229 add(binomial(n-2*k-1,n-4*k) * binomial(2*k,k) / (k+1),k=0..floor(n/4)) ;
%p A361229 end proc:
%p A361229 seq(A361229(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A361229 (PARI) a(n) = sum(k=0, n\4, binomial(n-2*k-1, n-4*k)*binomial(2*k, k)/(k+1));
%Y A361229 Partial sums give A023426.
%Y A361229 Cf. A002026, A006319, A052702.
%K A361229 nonn
%O A361229 0,6
%A A361229 _Seiichi Manyama_, Oct 15 2023