OFFSET
0,2
COMMENTS
The signed sequence (-1)^C(n+1, 2)*a(n) with g.f. (1 - 6x + 12x^2 - 8x^3) / (1 + 24x^2 + 16x^4) is the Hankel transform of (-1)^C(n+1, 2)*A063886.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,24,0,-16).
FORMULA
G.f.: (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).
a(n) = 2^n*((((3 + 2*sqrt(2))^((n+1)/2) + (3-2*sqrt(2))^((n+1)/2))/2)(1 - (-1)^n)/2 + (((3 + 2*sqrt(2))^(n/2) + (3 - 2*sqrt(2))^(n/2))/2)(1 + (-1)^n)/2).
MATHEMATICA
CoefficientList[Series[(1 + 6 x - 12 x^2 - 8 x^3)/(1 - 24 x^2 + 16 x^4), {x, 0, 20}], x] (* Wesley Ivan Hurt, Mar 30 2017 *)
LinearRecurrence[{0, 24, 0, -16}, {1, 6, 12, 136}, 30] (* Harvey P. Dale, Jul 16 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Aug 17 2009
STATUS
approved