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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 13:49 EDT 2021. Contains 348170 sequences. (Running on oeis4.)