A375169 Expansion of (1 - x) / ((1 - x)^3 - x^4).

1, 2, 3, 4, 6, 11, 22, 43, 80, 144, 257, 462, 839, 1532, 2798, 5099, 9274, 16855, 30640, 55728, 101393, 184490, 335659, 610628, 1110790, 2020635, 3675822, 6686979, 12164896, 22130208, 40258737, 73237462, 133231279, 242370396, 440913550, 802098203, 1459155634

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Hùng Việt Chu and Zachary Louis Vasseur, Linear Recurrences of Generalized Schreier Sets Revisited, J. Int. Seq. 29 (2026), Article 26.2.2. See p. 3 (Table 2).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1).

Formula

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

a(n) = Sum_{k=0..floor(n/4)} binomial(n+1-k,n-4*k).

a(n) = (n + 1)*hypergeom([(1-n)/4, (2-n)/4, (3-n)/4, -n/4], [2/3, 4/3, -1-n], -4^4/3^3). - Stefano Spezia, Jun 18 2025

Prog

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

Crossrefs

Cf. A024494, A052921, A124820, A137357.

Cf. A003522, A107068.

Sequence in context: A016038 A384155 A003099 * A061941 A029505 A185092

Adjacent sequences: A375166 A375167 A375168 * A375170 A375171 A375172

Keyword

nonn,easy

Author

Seiichi Manyama, Aug 05 2024

Status

approved