A135153 Repeat Pell numbers A000129.

0, 0, 1, 1, 2, 2, 5, 5, 12, 12, 29, 29, 70, 70, 169, 169, 408, 408, 985, 985, 2378, 2378, 5741, 5741, 13860, 13860, 33461, 33461, 80782, 80782, 195025, 195025, 470832, 470832, 1136689, 1136689, 2744210, 2744210, 6625109, 6625109, 15994428, 15994428, 38613965

Offset: 0

Author

Paul Curtz, Feb 14 2008

Keywords

• nonn
• easy

Comments

The binomial transform is 0, 0, 1, 4, 12, 32,... (n>=0), i.e. A135248 without one of the leading zeros. - R. J. Mathar, Jul 10 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,1)

Programs

Magma

I:=[0,0,1,1]; [n le 4 select I[n] else 2*Self(n-2)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, Mar 03 2014

Mathematica

CoefficientList[Series[x^2 (1 + x)/(1 - 2 x^2 - x^4), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 03 2014 *)
LinearRecurrence[{0,2,0,1},{0,0,1,1},50] (* Harvey P. Dale, May 28 2023 *)

Formula

G.f.: x^2*(1+x)/(1-2*x^2-x^4). - Philippe Deléham, Feb 25 2014

a(n) = 2*a(n-2) + a(n-4), a(0) = a(1) = 0, a(2) = a(3) = 1. - Philippe Deléham, Feb 25 2014

Extensions

Corrected and extended by Vincenzo Librandi, Mar 03 2014