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

0,5

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)

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A184307 A032580 A002014 * A097896 A030223 A300436

Adjacent sequences: A135150 A135151 A135152 * A135154 A135155 A135156

Keyword

nonn,easy

Author

Paul Curtz, Feb 14 2008

Extensions

Corrected and extended by Vincenzo Librandi, Mar 03 2014

Status

approved