A001447 a(n) = (5^n + 5^floor(n/2))/2.

1, 3, 15, 65, 325, 1575, 7875, 39125, 195625, 976875, 4884375, 24415625, 122078125, 610359375, 3051796875, 15258828125, 76294140625, 381469921875, 1907349609375, 9536744140625, 47683720703125

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (5,5,-25).

Programs

Mathematica

Table[(5^n+5^Floor[n/2])/2,{n,0,20}] (* or *) LinearRecurrence[ {5,5,-25}, {1,3,15}, 50](* Harvey P. Dale, May 05 2011 *)

PARI

a(n)=(5^n+5^(n\2))/2 \\ Charles R Greathouse IV, Apr 17 2012

Formula

a(n) = 5*a(n-1) + 5*a(n-2) - 25*a(n-3); a(0)=1, a(1)=3, a(2)=15. - Harvey P. Dale, May 05 2011

G.f.: (1 - 2x - 5x^2)/(1 - 5x - 5x^2 + 25x^3). - Harvey P. Dale, May 05 2011