A373910 Number of compositions of 7*n into parts 4 and 7.
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
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-34,21,-7,1).
Programs
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PARI
a(n) = sum(k=0, n\4, binomial(n+3*k, n-4*k));
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).