A082412 a(n) = (2*8^n + 2^n)/3.

1, 6, 44, 344, 2736, 21856, 174784, 1398144, 11184896, 89478656, 715828224, 5726623744, 45812985856, 366503878656, 2932031012864, 23456248070144, 187649984495616, 1501199875833856, 12009599006408704, 96076792050745344, 768614336404914176

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083076.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..250
• Index entries for linear recurrences with constant coefficients, signature (10,-16).

Crossrefs

Cf. A082413.

Programs

Maple

seq((2*8^n+2^n)/3,n=0..20); # Nathaniel Johnston, Jun 26 2011

Mathematica

Table[(2*8^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{10,-16},{1,6},30] (* Harvey P. Dale, Sep 30 2018 *)

PARI

a(n)=(2*8^n+2^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

Python

def A082412(n): return (2<<(n<<1)|1)//3<Chai Wah Wu, Apr 25 2025

Formula

G.f.: (1-4*x)/((1-2*x)*(1-8*x));

E.g.f.: (2*exp(8*x) + exp(2*x))/3.

a(n) = (2*8^n + 2^n)/3.

a(n) = 2^n*A001045(2n+1). - Paul Barry, Sep 10 2007