A375169 Expansion of (1 - x) / ((1 - x)^3 - x^4).
1, 2, 3, 4, 6, 11, 22, 43, 80, 144, 257, 462, 839, 1532, 2798, 5099, 9274, 16855, 30640, 55728, 101393, 184490, 335659, 610628, 1110790, 2020635, 3675822, 6686979, 12164896, 22130208, 40258737, 73237462, 133231279, 242370396, 440913550, 802098203, 1459155634
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1).
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec((1-x)/((1-x)^3-x^4))
Formula
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+1-k,n-4*k).
a(n) = (n + 1)*hypergeom([(1-n)/4, (2-n)/4, (3-n)/4, -n/4], [2/3, 4/3, -1-n], -4^4/3^3). - Stefano Spezia, Jun 18 2025