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A092688 Row sums of triangle A092686, in which the convolution of each row with {1,2} produces a triangle that, when flattened, equals the flattened form of A092686. 2
1, 4, 16, 58, 204, 698, 2346, 7774, 25480, 82774, 266946, 855674, 2728702, 8663402, 27400862, 86376186, 271488444, 851099874, 2661967502, 8308462182, 25883429326, 80497346294, 249956869434, 775048966478, 2400067860090 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f.: A(x) = H(x)*(1-x)/(1-3*x), where H(x) satisfies: H(x) = H(x^2/(1-2x))/(1-2x) and H(x) is the g.f. of A092687. - 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, 2, if(k==n, T(n, 0), 2*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+2*x, d=1, G=x, H=1+2*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, d*n, polcoeff(polcoeff(A, n, x), k, y))} \\ Paul D. Hanna, Jul 17 2006

CROSSREFS

Cf. A092683, A092686, A092687, A092689.

Sequence in context: A263851 A126644 A168583 * A267466 A255299 A123889

Adjacent sequences:  A092685 A092686 A092687 * A092689 A092690 A092691

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 04 2004

STATUS

approved

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Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)