A081656 a(n) = 2*6^n - 2^n.

1, 10, 68, 424, 2576, 15520, 93248, 559744, 3358976, 20154880, 120931328, 725592064, 4353560576, 26121379840, 156728311808, 940369936384, 5642219749376, 33853318758400, 203119913074688, 1218719479496704, 7312316879077376, 43873901278658560, 263243407680339968

Offset: 0

Author

Paul Barry, Mar 26 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081655.

Inverse binomial transform of A081657.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-12).

Crossrefs

Third column of array A094424.

Cf. A081655, A081657.

Programs

Magma

[2*6^n-2^n: n in [0..30]]; // Vincenzo Librandi, Aug 10 2013

Mathematica

CoefficientList[Series[(1 + 2 x) / ((1 - 6 x) (1 - 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
Table[2*6^n-2^n,{n,0,20}] (* or *) LinearRecurrence[{8,-12},{1,10},20] (* Harvey P. Dale, Mar 17 2019 *)

PARI

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

Formula

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

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

a(0)=1, a(2)=10; for n>2, a(n) = 8*a(n-1) - 12*a(n-2). - Vincenzo Librandi, Aug 10 2013