A373909 Number of compositions of 7*n into parts 3 and 7.
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
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,36,-35,21,-7,1).
Programs
-
PARI
a(n) = sum(k=0, n\3, binomial(n+4*k, n-3*k));
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).