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A369837
Number of compositions of 5*n-2 into parts 1 and 5.
5
1, 5, 20, 80, 325, 1326, 5411, 22076, 90061, 367411, 1498887, 6114853, 24946129, 101770120, 415180936, 1693770328, 6909898016, 28189589705, 115002126790, 469162173146, 1913991948274, 7808313175575, 31854760257925, 129954540535600, 530161974821876
OFFSET
1,2
FORMULA
a(n) = A003520(5*n-2).
a(n) = Sum_{k=0..n} binomial(n+2+4*k,n-1-k).
a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(1-x)/((1-x)^5 - x).
MATHEMATICA
LinearRecurrence[{6, -10, 10, -5, 1}, {1, 5, 20, 80, 325}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+2+4*k, n-1-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved