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A369849
Number of compositions of 5*n-1 into parts 4 and 5.
4
1, 2, 3, 4, 6, 13, 35, 92, 220, 484, 1013, 2092, 4382, 9404, 20552, 45185, 99009, 215481, 466361, 1006897, 2174834, 4705895, 10200142, 22128873, 48009456, 104111224, 225655617, 488945055, 1059372394, 2295532150, 4974876116, 10782658417, 23371307904, 50655960304
OFFSET
1,2
FORMULA
a(n) = A017827(5*n-1).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-1-4*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*(1-x)^3/((1-x)^5 - x^4).
MATHEMATICA
LinearRecurrence[{5, -10, 10, -4, 1}, {1, 2, 3, 4, 6}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n+k, n-1-4*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved