A083301 a(n) = (4*8^n + (-2)^n)/5.

1, 6, 52, 408, 3280, 26208, 209728, 1677696, 13421824, 107374080, 858993664, 6871947264, 54975582208, 439804649472, 3518437212160, 28147497664512, 225179981381632, 1801439850921984, 14411518807638016, 115292150460579840

Offset: 0

Author

Paul Barry, Apr 24 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083300.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (6,16).

Crossrefs

Cf. A083302.

Programs

Magma

[(4*8^n+(-2)^n)/5: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

Mathematica

Table[(4 * 8^n + (-2)^n)/5, {n, 0, 19}] (* Alonso del Arte, Mar 29 2011 *)

PARI

a(n)=4^(n+1)\/5<Charles R Greathouse IV, Jun 29 2011

Sage

[lucas_number1(n,6,-16) for n in range(1, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

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

E.g.f.: (4*exp(8*x) + exp(-2*x))/5.