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

0,3

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).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A369803, A369842, A369843, A369844.

Cf. A099131, A369836, A369845.

Cf. A001687.

Sequence in context: A272819 A185250 A048496 * A210581 A037488 A129669

Adjacent sequences: A369837 A369838 A369839 * A369841 A369842 A369843

Keyword

nonn

Author

Seiichi Manyama, Feb 03 2024

Status

approved