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A373909
Number of compositions of 7*n into parts 3 and 7.
5
1, 1, 1, 2, 9, 37, 122, 346, 913, 2398, 6515, 18317, 52226, 148408, 417810, 1168085, 3258813, 9103828, 25488736, 71462437, 200406479, 561770980, 1573939555, 4408629727, 12348599802, 34592601763, 96916209910, 271537125048, 760777555986, 2131439888257
OFFSET
0,4
FORMULA
a(n) = A369814(7*n).
a(n) = Sum_{k=0..floor(n/3)} binomial(n+4*k,n-3*k).
a(n) = 7*a(n-1) - 21*a(n-2) + 36*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 1/(1 - x - x^3/(1 - x)^6).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n+4*k, n-3*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved