A012493 Take every 5th term of Padovan sequence A000931, beginning with the fifth term.

0, 2, 9, 37, 151, 616, 2513, 10252, 41824, 170625, 696081, 2839729, 11584946, 47261895, 192809420, 786584466, 3208946545, 13091204281, 53406819691, 217878227876, 888855064897, 3626169232672, 14793304131648, 60350698792449, 246206446668325, 1004422742303477

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4,1).

Programs

Magma

I:=[0, 2, 9]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 17 2012

Mathematica

CoefficientList[Series[x*(2-x)/(1-5*x+4*x^2-x^3),{x,0,30}],x] (* Vincenzo Librandi, Apr 17 2012 *)
LinearRecurrence[{5,-4,1},{0,2,9},30] (* Harvey P. Dale, Nov 24 2018 *)

Formula

a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).

G.f.: x*(2-x)/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 02 2012

Extensions

First term corrected by Colin Barker, Feb 02 2012