OFFSET
0,2
COMMENTS
3rd binomial transform of 1,0,1,0,2,0,4,0,8,0,...
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..1500
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
E.g.f.: exp(3*x)*cosh(x/sqrt(2))^2. - Stefano Spezia, May 11 2024
MATHEMATICA
LinearRecurrence[{9, -25, 21}, {1, 3, 10}, 26] (* Stefano Spezia, May 11 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 17 2009
STATUS
approved