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A369850
Number of compositions of 5*n-2 into parts 4 and 5.
4
0, 1, 3, 6, 10, 16, 29, 64, 156, 376, 860, 1873, 3965, 8347, 17751, 38303, 83488, 182497, 397978, 864339, 1871236, 4046070, 8751965, 18952107, 41080980, 89090436, 193201660, 418857277, 907802332, 1967174726, 4262706876, 9237582992, 20020241409, 43391549313
OFFSET
1,3
FORMULA
a(n) = A017827(5*n-2).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-2-4*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^2*(1-x)^2/((1-x)^5 - x^4).
MATHEMATICA
LinearRecurrence[{5, -10, 10, -4, 1}, {0, 1, 3, 6, 10}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n+k, n-2-4*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved