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)).

1, 2, 3, 5, 8, 14, 24, 44, 79, 149, 275, 527, 989, 1913, 3629, 7061, 13496, 26366, 50676, 99296, 191674, 376430, 729146, 1434578, 2786656, 5490812, 10691112, 21091712, 41150012, 81266612, 158825372, 313942892, 614483087, 1215563477

Offset: 1

Author

Benoit Cloitre, Jul 30 2002

Keywords

• easy
• nonn

Comments

Partial sums of A001405, to which an additional leading 1 is added. - Paul Barry, Oct 12 2004

Crossrefs

Cf. A036256.

Formula

G.f.: 1/2*x*(((1+2*x)/(1-2*x))^(1/2)-1)/(1-x)-1. - Vladeta Jovovic, Jan 15 2004

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

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