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 A072100 #17 Jan 09 2025 04:08:13
%S A072100 1,2,3,5,8,14,24,44,79,149,275,527,989,1913,3629,7061,13496,26366,
%T A072100 50676,99296,191674,376430,729146,1434578,2786656,5490812,10691112,
%U A072100 21091712,41150012,81266612,158825372,313942892,614483087,1215563477
%N A072100 Column 2 of the array m(i,1)=m(1,j)=1 m(i,j)=m(i-1,j-1)+m(i-1,j+1) (a(n)=m(n,2)).
%C A072100 Partial sums of A001405, to which an additional leading 1 is added. - _Paul Barry_, Oct 12 2004
%F A072100 G.f.: 1/2*x*(((1+2*x)/(1-2*x))^(1/2)-1)/(1-x)-1. - _Vladeta Jovovic_, Jan 15 2004
%F A072100 G.f.: x*(sqrt(1+2*x)+1/sqrt(1-2*x))/((1-x)*(sqrt(1+2*x)+sqrt(1-2*x))); a(n) = 1+Sum_{k=0..n-2} binomial(k, floor(k/2)). - _Paul Barry_, Oct 12 2004
%F A072100 Conjecture: (-n+1)*a(n) +(n+1)*a(n-1) +2*(2*n-7)*a(n-2) +4*(-n+3)*a(n-3)=0. - _R. J. Mathar_, Nov 26 2012
%Y A072100 Cf. A036256.
%K A072100 easy,nonn
%O A072100 1,2
%A A072100 _Benoit Cloitre_, Jul 30 2002