A335087 Row sums of A335436.

1, 7, 34, 150, 628, 2540, 10024, 38840, 148368, 560368, 2096928, 7786592, 28726592, 105390272, 384788096, 1398978432, 5067403520, 18294707968, 65854095872, 236421150208, 846732997632, 3025927678976, 10792083499008, 38420157773824, 136547503083520, 484546494459904, 1716976084393984

Offset: 0

Author

Oboifeng Dira, Sep 11 2020

Keywords

• nonn

Comments

This sequence is also a composition of generating functions H(x) = G(F(x)), where G(x) = x/(1-4*x)^2 is the generating function of A002697 and F(x) = x*(1-x)/(1-2*x^2) is the generating function of 0, A016116*(-1)^n.

Examples

			For n = 4, a(4) = 8*a(3)-20*a(2)+16*a(1)-4*a(0) = 8*150-20*34+16*7-4*1 = 628.
		

Links

• Oboifeng Dira, A Note on Composition and Recursion, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Crossrefs

Composition of g.fs of A002697 and A016116.

Cf. A335436.

Programs

Maple

f:=x->x*(1-x)/(1-2*x^2):g:=x->(x)/(1-4*x)^2:
C:=n->coeff(series(g(f(x))/x,x,n+1),x,n): seq(C(n),n=0..30);

Formula

a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-4*a(n-4), a(0)=1, a(1)=7, a(2)=34, a(3)=150 for n>=4.

G.f.: (1-x)*(1-2*x^2)/(1-4*x+2*x^2)^2.

a(0)=1; a(n) = 2*n+1+Sum_{k=1..n}[(2+sqrt(2))^(k+1)-(2-sqrt(2))^(k+1)]*(2n-k+1)/(4*sqrt(2)), n>=1.

G.f.: G(F(x))/x where G(x) is g.f of A002697 and F(x) is g.f of 0,A016116*(-1)^n.