A387625 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k).
1, 1, 1, 7, 21, 43, 93, 251, 661, 1587, 3805, 9499, 23813, 58691, 144141, 356491, 883637, 2184115, 5391869, 13325371, 32953317, 81459235, 201299565, 497518187, 1229819541, 3039854611, 7513347421, 18570354203, 45900859333, 113454099843, 280422868685
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-1,4,4,0,-4).
Programs
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PARI
a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k+1, 2*k));
Formula
G.f.: (1-x+2*x^3)/((1-x+2*x^3)^2 - 8*x^3).
a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).