A199215 a(n) = 4*5^n + 1.

5, 21, 101, 501, 2501, 12501, 62501, 312501, 1562501, 7812501, 39062501, 195312501, 976562501, 4882812501, 24414062501, 122070312501, 610351562501, 3051757812501, 15258789062501, 76293945312501, 381469726562501, 1907348632812501, 9536743164062501, 47683715820312501

Offset: 0

Author

Vincenzo Librandi, Nov 04 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Programs

Magma

[4*5^n+1: n in [0..30]];

Mathematica

4*5^Range[0,30]+1 (* or *) LinearRecurrence[{6,-5},{5,21},30] (* Harvey P. Dale, Mar 30 2018 *)

Formula

a(n) = 5*a(n-1) - 4.

a(n) = 6*a(n-1) - 5*a(n-2).

G.f.: (5-9*x)/((1-x)*(1-5*x)). - Bruno Berselli, Nov 04 2011

E.g.f.: exp(x)*(1 + 4*exp(4*x)). - Elmo R. Oliveira, May 07 2025