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A369846
Number of compositions of 5*n-1 into parts 3 and 5.
5
0, 1, 4, 10, 21, 44, 101, 250, 629, 1557, 3784, 9120, 21992, 53228, 129177, 313701, 761403, 1846804, 4478044, 10858285, 26332515, 63865592, 154900529, 375691009, 911166977, 2209835169, 5359470121, 12998281146, 31524747503, 76457088518, 185431544730
OFFSET
1,3
FORMULA
a(n) = A052920(5*n-1).
a(n) = Sum_{k=0..floor(n/3)} binomial(n+1+2*k,n-2-3*k).
a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x^2*(1-x)/((1-x)^5 - x^3).
MATHEMATICA
LinearRecurrence[{5, -10, 11, -5, 1}, {0, 1, 4, 10, 21}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n+1+2*k, n-2-3*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved