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.
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
Offset: 0
Keywords
Programs
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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
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