A369845 Number of compositions of 5*n into parts 3 and 5.

1, 1, 1, 2, 7, 22, 58, 138, 319, 750, 1810, 4427, 10828, 26349, 63862, 154603, 374521, 908140, 2203162, 5344988, 12964858, 31443013, 76253683, 184929945, 448506736, 1087774536, 2638209313, 6398479259, 15518219326, 37636240539, 91279009255, 221378866489

Offset

0,4

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = Sum_{k=0..floor(n/3)} binomial(n+2*k,n-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.: (1-x)^4/((1-x)^5 - x^3).

a(n) = A369847(n+1)-A369847(n). - R. J. Mathar, Feb 14 2024

Mathematica

LinearRecurrence[{5, -10, 11, -5, 1}, {1, 1, 1, 2, 7}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

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

Crossrefs

Cf. A369804, A369846, A369847, A369848.

Cf. A052920.

Sequence in context: A371716 A063019 A386203 * A365756 A183156 A389131

Adjacent sequences: A369842 A369843 A369844 * A369846 A369847 A369848

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved