A081626 2*6^n-4^n.

1, 8, 56, 368, 2336, 14528, 89216, 543488, 3293696, 19893248, 119883776, 721399808, 4336787456, 26054279168, 156459892736, 939296227328, 5637924847616, 33836139020288, 203051193860096, 1218444602114048

Offset: 0

Author

Paul Barry, Mar 25 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081625. Inverse binomial transform of A081627.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-24).

Programs

Magma

[2*6^n-4^n: n in [0..25]]; // Vincenzo Librandi, Aug 09 2013

Mathematica

Table[2 6^n - 4^n, {n, 0, 20}] (* or *) LinearRecurrence[{10, -24}, {1, 8}, 20] (* Harvey P. Dale, Aug 19 2012 *)
CoefficientList[Series[(1 - 2 x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)

PARI

a(n)=2*6^n-4^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 10*a(n-1)-24*a(n-2), a(0)=1, a(1)=8.

G.f.: (1-2*x)/((1-4*x)(1-6*x)).

E.g.f. 2*exp(6*x)-exp(4*x).