A097111 Expansion of (1 + 3x - 2x^2 - 12x^3)/(1 - 9x^2 + 20x^4).
1, 3, 7, 15, 43, 75, 247, 375, 1363, 1875, 7327, 9375, 38683, 46875, 201607, 234375, 1040803, 1171875, 5335087, 5859375, 27199723, 29296875, 138095767, 146484375, 698867443, 732421875, 3527891647, 3662109375, 17773675963, 18310546875
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,9,0,-20).
Formula
G.f.: 3*(1+x)/(1-5x^2) - 2/(1-4x^2);
a(n) = 9*a(n-2) - 20*a(n-4);
a(n) = (3/2 + 3*sqrt(5)/10)*(sqrt(5))^n + (3/2 - 3*sqrt(5)/10)*(-sqrt(5))^n - 2^(n+1)*(1+(-1)^n)/2;
a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))*2^k.