A369846 Number of compositions of 5*n-1 into parts 3 and 5.

0, 1, 4, 10, 21, 44, 101, 250, 629, 1557, 3784, 9120, 21992, 53228, 129177, 313701, 761403, 1846804, 4478044, 10858285, 26332515, 63865592, 154900529, 375691009, 911166977, 2209835169, 5359470121, 12998281146, 31524747503, 76457088518, 185431544730

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,11,-5,1).

Formula

a(n) = A052920(5*n-1).

a(n) = Sum_{k=0..floor(n/3)} binomial(n+1+2*k,n-2-3*k).

a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: x^2*(1-x)/((1-x)^5 - x^3).

Mathematica

LinearRecurrence[{5, -10, 11, -5, 1}, {0, 1, 4, 10, 21}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n+1+2*k, n-2-3*k));

Crossrefs

Cf. A369804, A369845, A369847, A369848.

Cf. A052920.

Sequence in context: A111927 A329361 A290998 * A227803 A109885 A054211

Adjacent sequences: A369843 A369844 A369845 * A369847 A369848 A369849

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved