A390044 Expansion of 1 / ((1-x)^4 - x^5).

1, 4, 10, 20, 35, 57, 92, 156, 285, 550, 1079, 2092, 3965, 7359, 13485, 24633, 45185, 83488, 155248, 289656, 540536, 1006897, 1871236, 3471298, 6434484, 11928731, 22128873, 41080980, 76302420, 141745045, 263289438, 488945055, 907802332, 1685254125, 3128438335

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1).

Formula

a(n) = Sum_{k=0..floor(n/5)} binomial(n-k+3,n-5*k).

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

Mathematica

LinearRecurrence[{4, -6, 4, -1, 1}, {1, 4, 10, 20, 35}, 50] (* Vincenzo Librandi, Jan 16 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^4-x^5))
(Magma) I:=[1, 4, 10, 20, 35]; [n le 5 select I[n] else 4*Self(n-1) - 6*Self(n-2) + 4*Self(n-3) - Self(n-4) + Self(n-5): n in [1..40]]; // Vincenzo Librandi, Jan 16 2026

Crossrefs

Cf. A000749, A369794, A390045.

Sequence in context: A057319 A034223 A266353 * A139748 A373963 A392553

Adjacent sequences: A390041 A390042 A390043 * A390045 A390046 A390047

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 15 2026

Status

approved