A397234 - OEIS

A397234

Expansion of 1/(1 - x - x^2 + x^3 - x^5 - x^6).

1, 1, 2, 2, 3, 4, 7, 11, 18, 27, 41, 61, 93, 142, 219, 336, 515, 786, 1200, 1832, 2801, 4284, 6554, 10023, 15325, 23427, 35814, 54754, 83718, 128006, 195722, 299251, 457535, 699536, 1069544, 1635273, 2500254, 3822769, 5844821, 8936416, 13663285, 20890407, 31940299, 48835011

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,1).

FORMULA

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) + a(n-6).

G.f.: 1/( (1+x) * (1-2*x+x^2-x^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=5, k=1, P(x)=1+x, Q(x)=1-x, R(x)=1, and b(n) = A397233(n). Therefore a(n) = b(2*n+5) = A397233(2*n+5), and Sum_{n>=0} a(n) * x^n = 1/(1 - x - x^2 + x^3 - x^5 - x^6).

PROG

(PARI) my(N=50, x='x+O('x^N)); Vec(1/(1-x-x^2+x^3-x^5-x^6))

CROSSREFS

Cf. A397233.

Sequence in context: A059348 A110871 A243856 * A173433 A389122 A053638

Adjacent sequences: A397231 A397232 A397233 * A397235 A397236 A397237

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 19 2026

STATUS

approved