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A373959
Number of compositions of 6*n-4 into parts 1 and 6.
3
1, 4, 16, 71, 322, 1455, 6558, 29548, 133146, 599998, 2703794, 12184181, 54905857, 247423522, 1114970351, 5024416818, 22641646338, 102030577247, 459782762029, 2071929748572, 9336785189996, 42074572144477, 189601622519548, 854406199035948, 3850230516227419
OFFSET
1,2
FORMULA
a(n) = A005708(6*n-4).
a(n) = Sum_{k=0..n} binomial(n+1+5*k,n-1-k).
a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
G.f.: x*(1-x)^3/((1-x)^6 - x).
a(n) = A373958(n) - A373958(n-1).
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+1+5*k, n-1-k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 23 2024
STATUS
approved