A369843 Number of compositions of 5*n-3 into parts 2 and 5.

1, 2, 4, 11, 34, 102, 296, 851, 2452, 7085, 20489, 59241, 171245, 494973, 1430710, 4135527, 11953991, 34553692, 99879234, 288705927, 834519021, 2412219633, 6972643768, 20154781952, 58258423000, 168398935968, 486765693153, 1407021006061, 4067065818560

Offset: 1

Author

Seiichi Manyama, Feb 03 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A369803, A369840, A369842, A369844.

Cf. A001687.

Programs

Mathematica

LinearRecurrence[{5, -9, 10, -5, 1}, {1, 2, 4, 11, 34}, 50] (* Paolo Xausa, Mar 15 2024 *)

PARI

a(n) = sum(k=0, n\2, binomial(n+3*k, n-1-2*k));

Formula

a(n) = A001687(5*n-2).

a(n) = Sum_{k=0..floor(n/2)} binomial(n+3*k,n-1-2*k).

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

G.f.: x*(1-x)^3/((1-x)^5 - x^2).