A369849 Number of compositions of 5*n-1 into parts 4 and 5.

1, 2, 3, 4, 6, 13, 35, 92, 220, 484, 1013, 2092, 4382, 9404, 20552, 45185, 99009, 215481, 466361, 1006897, 2174834, 4705895, 10200142, 22128873, 48009456, 104111224, 225655617, 488945055, 1059372394, 2295532150, 4974876116, 10782658417, 23371307904, 50655960304

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,-10,10,-4,1).

Formula

a(n) = A017827(5*n-1).

a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-1-4*k).

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

G.f.: x*(1-x)^3/((1-x)^5 - x^4).

Mathematica

LinearRecurrence[{5, -10, 10, -4, 1}, {1, 2, 3, 4, 6}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n+k, n-1-4*k));

Crossrefs

Cf. A099131, A368475, A369850, A369851.

Cf. A017827.

Sequence in context: A038767 A363198 A188715 * A174046 A095991 A293714

Adjacent sequences: A369846 A369847 A369848 * A369850 A369851 A369852

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved