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

0,2

Links

Table of n, a(n) for n=0..29.

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.

Crossrefs

Cf. A005053 (bisection), A193656 (bisection?).

Sequence in context: A146033 A147188 A050565 * A371914 A151401 A080567

Adjacent sequences: A097108 A097109 A097110 * A097112 A097113 A097114

Keyword

easy,nonn

Author

Paul Barry, Jul 25 2004

Status

approved