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

0,2

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.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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).

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.

Example

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.

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);

Mathematica

LinearRecurrence[{8, -20, 16, -4}, {1, 7, 34, 150}, 30] (* Paolo Xausa, Jul 06 2026 *)

Crossrefs

Composition of g.fs of A002697 and A016116.

Cf. A335436.

Sequence in context: A052161 A080960 A243414 * A213119 A099242 A032206

Adjacent sequences: A335084 A335085 A335086 * A335088 A335089 A335090

Keyword

nonn,easy,changed

Author

Oboifeng Dira, Sep 11 2020

Status

approved