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 A371872 #10 Apr 22 2024 12:33:17
%S A371872 1,1,3,11,40,147,547,2055,7777,29602,113204,434591,1673821,6464539,
%T A371872 25026534,97087873,377329971,1468856383,5726159811,22351657810,
%U A371872 87350137071,341726039806,1338173763288,5244830032639,20573285744475,80761011408961,317249771957040
%N A371872 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k-1,n-3*k).
%F A371872 a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(n-1)).
%F A371872 D-finite with recurrence +n*a(n) +(-15*n+14)*a(n-1) +3*(27*n-50)*a(n-2) +2*(-93*n+259)*a(n-3) +24*(7*n-26)*a(n-4) +(-69*n+260)*a(n-5) +10*(2*n-9)*a(n-6)=0. - _R. J. Mathar_, Apr 22 2024
%p A371872 A371872 := proc(n)
%p A371872 add(binomial(2*n-2*k-1,n-3*k),k=0..floor(n/3)) ;
%p A371872 end proc:
%p A371872 seq(A371872(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A371872 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k-1, n-3*k));
%Y A371872 Cf. A360150, A371871, A371873.
%Y A371872 Cf. A144904, A371842.
%K A371872 nonn
%O A371872 0,3
%A A371872 _Seiichi Manyama_, Apr 10 2024