A369847 Number of compositions of 5*n-2 into parts 3 and 5.

1, 2, 3, 5, 12, 34, 92, 230, 549, 1299, 3109, 7536, 18364, 44713, 108575, 263178, 637699, 1545839, 3749001, 9093989, 22058847, 53501860, 129755543, 314685488, 763192224, 1850966760, 4489176073, 10887655332, 26405874658, 64042115197, 155321124452

Offset

1,2

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-2).

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

Mathematica

LinearRecurrence[{5, -10, 11, -5, 1}, {1, 2, 3, 5, 12}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

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

Crossrefs

Cf. A369804, A369845, A369846, A369848.

Cf. A052920.

Sequence in context: A319912 A153987 A228905 * A306038 A008323 A000997

Adjacent sequences: A369844 A369845 A369846 * A369848 A369849 A369850

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved