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A373910
Number of compositions of 7*n into parts 4 and 7.
5
1, 1, 1, 1, 2, 9, 37, 121, 332, 808, 1837, 4113, 9497, 23091, 58462, 150129, 382810, 960520, 2373982, 5816480, 14230964, 34948927, 86295036, 213973997, 531470618, 1319411997, 3270186871, 8091796123, 20002405065, 49435009494, 122222402392, 302354237393
OFFSET
0,5
FORMULA
a(n) = A369815(7*n).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+3*k,n-4*k).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 34*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 1/(1 - x - x^4/(1 - x)^6).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n+3*k, n-4*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved