A369848 Number of compositions of 5*n-4 into parts 3 and 5.

0, 1, 3, 6, 11, 23, 57, 149, 379, 928, 2227, 5336, 12872, 31236, 75949, 184524, 447702, 1085401, 2631240, 6380241, 15474230, 37533077, 91034937, 220790480, 535475968, 1298668192, 3149634952, 7638811025, 18526466357, 44932341015, 108974456212, 264295580664

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-4).

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

Mathematica

LinearRecurrence[{5, -10, 11, -5, 1}, {0, 1, 3, 6, 11}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

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

Crossrefs

Cf. A369804, A369845, A369846, A369847.

Cf. A052920.

Sequence in context: A045693 A051284 A319910 * A346050 A319636 A001867

Adjacent sequences: A369845 A369846 A369847 * A369849 A369850 A369851

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved