A164584 Expansion of (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).

1, 6, 12, 136, 272, 3168, 6336, 73856, 147712, 1721856, 3443712, 40142848, 80285696, 935878656, 1871757312, 21818802176, 43637604352, 508677193728, 1017354387456, 11859151814656, 23718303629312, 276480808452096

Offset: 0

Author

Paul Barry, Aug 17 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A063886.

Programs

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 *)

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).