A375278 Expansion of 1/((1 - x - x^3)^2 - 4*x^4).
1, 2, 3, 6, 15, 34, 70, 146, 317, 690, 1480, 3162, 6788, 14608, 31395, 67392, 144701, 310854, 667793, 1434310, 3080542, 6616676, 14212315, 30526804, 65567936, 140832740, 302495240, 649730544, 1395554885, 2997508382, 6438345511, 13828920758, 29703127299
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-1,2,2,0,-1).
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(1/((1-x-x^3)^2-4*x^4)) -
PARI
a(n) = sum(k=0, n\3, binomial(2*n-4*k+2, 2*k+1))/2;
Formula
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).
a(n) = (1/2) * Sum_{k=0..floor(n/3)} binomial(2*n-4*k+2,2*k+1).