A092685 Row sums of triangle A092683, in which the convolution of each row with {1,1} produces a triangle that, when flattened, equals the flattened form of A092683.

1, 2, 5, 11, 25, 55, 120, 258, 551, 1169, 2469, 5193, 10885, 22746, 47404, 98553, 204443, 423259, 874680, 1804556, 3717348, 7647075, 15711194, 32242013, 66096274, 135366764, 276988466, 566312984, 1156974619, 2362043602

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Formula

G.f.: A(x,y) = H(x)*(1-x)/(1-2*x), where H(x) satisfies: H(x) = H(x^2/(1-x))/(1-x) and H(x) is the g.f. of A092684. - Paul D. Hanna, Jul 17 2006

Prog

(PARI) {T(n, k)=if(n<0 || k>n, 0, if(n==0 && k==0, 1, if(n==1 && k<=1, 1, if(k==n, T(n, 0), T(n-1, k)+T(n-1, k+1)))))}
a(n)=sum(k=0, n, T(n, k))
(PARI) {a(n)=local(A, F=1+x, d=1, G=x, H=1+x, S=ceil(log(n+1)/log(d+1))); for(i=0, n, G=x*subst(F, x, G+x*O(x^n))); for(i=0, S, H=subst(H, x, x*G^d+x*O(x^n))*G/x); A=(x*H-y*subst(H, x, x*y^d +x*O(x^n)))/(x*subst(F, x, y)-y); sum(k=0, 2*n, polcoeff(polcoeff(A, n, x), k, y))} \\ Paul D. Hanna, Jul 17 2006

Crossrefs

Cf. A092683, A092684, A092686, A092689, A120897, A120902.

Sequence in context: A208739 A291737 A177795 * A172481 A151529 A192922

Adjacent sequences: A092682 A092683 A092684 * A092686 A092687 A092688

Keyword

nonn

Author

Paul D. Hanna, Mar 04 2004

Status

approved