A369851 Number of compositions of 5*n-3 into parts 4 and 5.

0, 0, 1, 4, 10, 20, 36, 65, 129, 285, 661, 1521, 3394, 7359, 15706, 33457, 71760, 155248, 337745, 735723, 1600062, 3471298, 7517368, 16269333, 35221440, 76302420, 165392856, 358594516, 777451793, 1685254125, 3652428851, 7915135727, 17152718719, 37172960128

Offset

1,4

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-3).

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

Mathematica

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

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n+k, n-3-4*k));

Crossrefs

Cf. A099131, A368475, A369849, A369850.

Cf. A017827.

Sequence in context: A000749 A360046 A354696 * A275934 A369693 A318338

Adjacent sequences: A369848 A369849 A369850 * A369852 A369853 A369854

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 03 2024

Status

approved