|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|