A369840 Number of compositions of 5*n into parts 2 and 5.

1, 1, 2, 7, 23, 68, 194, 555, 1601, 4633, 13404, 38752, 112004, 323728, 935737, 2704817, 7818464, 22599701, 65325542, 188826693, 545813094, 1577700612, 4560424135, 13182138184, 38103641048, 110140512968, 318366757185, 920255312908, 2660044812499, 7688994894381

Offset: 0

Author

Seiichi Manyama, Feb 03 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-9,10,-5,1).

Crossrefs

Cf. A369803, A369842, A369843, A369844.

Cf. A099131, A369836, A369845.

Cf. A001687.

Programs

Mathematica

LinearRecurrence[{5, -9, 10, -5, 1}, {1, 1, 2, 7, 23}, 50] (* Paolo Xausa, Mar 15 2024 *)

PARI

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

Formula

a(n) = A001687(5*n+1).

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

a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: (1-x)^4/((1-x)^5 - x^2).

a(n) = A369843(n) - A369843(n-1). - R. J. Mathar, Feb 14 2024