A397235 - OEIS

A397235

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

1, 2, 5, 11, 26, 60, 140, 325, 756, 1757, 4085, 9496, 22076, 51320, 119305, 277350, 644761, 1498887, 3484490, 8100456, 18831276, 43777405, 101770120, 236586825, 549997641, 1278589392, 2972359720, 6909898016, 16063564001, 37343255690, 86812537085, 201814663875

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..31.

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

FORMULA

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

G.f.: 1/( (1+x) * (1-3*x+2*x^2-x^3) ).

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=3, m=2, k=2, P(x)=1+x, Q(x)=1-x, R(x)=1, and b(n) = A079955(n). Therefore a(n) = b(3*n+4) = A079955(3*n+4), and Sum_{n>=0} a(n) * x^n = 1/(1 - 2*x - x^2 + x^3 - x^4).

PROG

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

CROSSREFS

Cf. A079955.

Sequence in context: A006138 A291930 A398790 * A238437 A191692 A182015

Adjacent sequences: A397232 A397233 A397234 * A397236 A397237 A397238

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 19 2026

STATUS

approved