A083222 a(n) = (4*5^n + (-5)^n)/5.

1, 3, 25, 75, 625, 1875, 15625, 46875, 390625, 1171875, 9765625, 29296875, 244140625, 732421875, 6103515625, 18310546875, 152587890625, 457763671875, 3814697265625, 11444091796875, 95367431640625, 286102294921875

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083297.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (0,25).

Crossrefs

Cf. A083223, A083299.

Programs

Magma

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

Mathematica

LinearRecurrence[{0,25},{1,3},30] (* or *) Riffle[NestList[25#&,1,10], NestList[ 25#&,3,10]] (* Harvey P. Dale, Dec 14 2017 *)

PARI

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

Formula

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

G.f.: (1+3*x)/((1+5*x)(1-5*x)).

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

Extensions

Edited by N. J. A. Sloane, Jun 08 2007