A171753 Expansion of 1/(1-3x-x^2/(1-3x-x^2/(1-3x))).

1, 3, 10, 36, 137, 543, 2218, 9264, 39329, 168939, 731770, 3188364, 13948745, 61196775, 269007994, 1184076216, 5216618369, 22996827795, 101421591466, 447422614068, 1974197123657, 8712062181999, 38449506441994

Offset

0,2

Comments

3rd binomial transform of 1,0,1,0,2,0,4,0,8,0,...

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (9,-25,21)

Formula

G.f.: (1-6x+8x^2)/(1-9x+25x^2-21x^3) = -(4*x-1)*(2*x-1) / ( (3*x-1)*(7*x^2-6*x+1) ).

a(n)=(3-sqrt(2))^n/4+(3+sqrt(2))^n/4+3^n/2.

a(n) = (3^n+A083878(n))/2. - R. J. Mathar, Oct 08 2016

Crossrefs

Sequence in context: A136576 A129156 A317775 * A002212 A340941 A149041

Adjacent sequences: A171750 A171751 A171752 * A171754 A171755 A171756

Keyword

easy,nonn

Author

Paul Barry, Dec 17 2009

Status

approved