A397237 - OEIS

A397237

Expansion of 1/(1 - 2*x + x^2 - x^3 - 2*x^4 - x^5).

1, 2, 3, 5, 11, 25, 52, 103, 206, 422, 870, 1782, 3631, 7400, 15113, 30891, 63113, 128879, 263162, 537453, 1097740, 2242060, 4579036, 9351820, 19099597, 39008270, 79668895, 162711793, 332313975, 678701189, 1386146256, 2830997779, 5781890234, 11808645298

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,2,1).

FORMULA

a(n) = 2*a(n-1) - a(n-2) + a(n-3) + 2*a(n-4) + a(n-5).

Let Sum_{n>=0} b(n) * x^n = 1/( P(x^s) * Q(x^s)^(s-1-k) * R(x^s)^k * (Q(x^s) - x^m * R(x^s)) ), where s >= 2, m >= 1, 0 <= k <= s-1, gcd(m,s)=1, and P(0)*Q(0)*R(0) != 0. Then Sum_{n>=0} b(s*n+m*k) * x^n = 1/( P(x) * (Q(x)^s - x^m * R(x)^s) ).

Here s=2, m=3, k=1, P(x)=1, Q(x)=1-x, R(x)=1+x, and b(n) = A397236(n). Therefore a(n) = b(2*n+3) = A397236(2*n+3), and Sum_{n>=0} a(n) * x^n = 1/(1 - 2*x + x^2 - x^3 - 2*x^4 - x^5).

MAPLE

a:= proc(n) option remember; `if`(n<1, 1+signum(n),

2*a(n-1)-a(n-2)+a(n-3)+2*a(n-4)+a(n-5))

end:

seq(a(n), n=0..33); # Alois P. Heinz, Jun 19 2026

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-2*x+x^2-x^3-2*x^4-x^5))

CROSSREFS

Cf. A397236.

Sequence in context: A060696 A076051 A000628 * A358554 A369495 A273755

Adjacent sequences: A397234 A397235 A397236 * A397238 A397240 A397241

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 19 2026

STATUS

approved