A375318 Expansion of 1/(1 - x^3*(1 + x)^4).
1, 0, 0, 1, 4, 6, 5, 9, 28, 57, 82, 122, 249, 519, 913, 1485, 2632, 5053, 9369, 16375, 28662, 52226, 96182, 173220, 307653, 551927, 1002327, 1815191, 3258813, 5845015, 10539893, 19048900, 34332648, 61735922, 111129005, 200406479, 361364501, 650804074, 1171717523
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,1,4,6,4,1).
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(1/(1-x^3*(1+x)^4)) -
PARI
a(n) = sum(k=0, n\3, binomial(4*k, n-3*k));
Formula
a(n) = a(n-3) + 4*a(n-4) + 6*a(n-5) + 4*a(n-6) + a(n-7).
a(n) = Sum_{k=0..floor(n/3)} binomial(4*k,n-3*k).