A081337 a(n) = (8^n + 4^n)/2.

1, 6, 40, 288, 2176, 16896, 133120, 1056768, 8421376, 67239936, 537395200, 4297064448, 34368126976, 274911461376, 2199157473280, 17592722915328, 140739635838976, 1125908496777216, 9007233614479360, 72057731476881408

Offset: 0

Author

Paul Barry, Mar 18 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081336. 6th binomial transform of (1,0,4,0,16,0,64,....).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (12,-32).

Crossrefs

Cf. A081338.

Programs

Magma

[(8^n+4^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013

Mathematica

CoefficientList[Series[(1 - 6 x) / ((1 - 4 x) (1 - 8 x)),{x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)

Formula

a(n) = 12*a(n-1) -32*a(n-2), a(0)=1, a(1)=6.

G.f.: (1-6*x)/((1-4*x)*(1-8*x)).

E.g.f.: exp(6*x) * cosh(2*x).