A396345 Expansion of x * (3+3*x-8*x^2-3*x^3+2*x^4-3*x^5+4*x^6+x^7-x^8)/((1-x)^2 * (1+x) * (1-3*x^2-x^4+x^6)).

3, 6, 10, 19, 31, 58, 96, 181, 303, 574, 966, 1835, 3095, 5886, 9936, 18905, 31923, 60750, 102594, 195251, 329751, 627578, 1059904, 2017213, 3406847, 6483942, 10950670, 20841435, 35198927, 66991006, 113140576, 215330481, 363669955, 692140982, 1168951482, 2224762387

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-2,2,-2,2,1,-1).

Formula

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) + a(n-8) - a(n-9).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(x*(3+3*x-8*x^2-3*x^3+2*x^4-3*x^5+4*x^6+x^7-x^8)/((1-x)^2*(1+x)*(1-3*x^2-x^4+x^6)))

Crossrefs

Cf. A396344, A396346.

Sequence in context: A373803 A132274 A253768 * A091714 A017991 A065614

Adjacent sequences: A396342 A396343 A396344 * A396346 A396347 A396348

Keyword

nonn,easy

Author

Seiichi Manyama, May 23 2026

Status

approved