A135248 -id:A135248 - cp's OEIS frontend

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

Paul Curtz, Feb 14 2008

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

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

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

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 *)

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

Corrected and extended by Vincenzo Librandi, Mar 03 2014

A101893 a(n) = Sum_{k=0..floor(n/2)} C(n,2k)*Pell(k).

Original entry on oeis.org

0, 0, 1, 3, 8, 20, 50, 126, 320, 816, 2084, 5324, 13600, 34736, 88712, 226552, 578560, 1477504, 3773200, 9635888, 24607872, 62842944, 160486688, 409846752, 1046656000, 2672922880, 6826040896, 17432165568, 44517810688, 113688426240

Offset: 0

Paul Barry, Dec 22 2004

Transform of Pell numbers under the mapping g(x)-> (1/(1-x))*g(x^2/((1-x)^2)).

Binomial transform of aerated Pell numbers 0,0,1,0,2,0,5,0,12,...

Andrew Woods, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2).

Cf. A000129 (Pell numbers), A135248 (partial sums).

CoefficientList[Series[x^2*(1-x)/(1 - 4*x + 4*x^2 - 2*x^4), {x, 0, 40}], x] (* Vaclav Kotesovec, Jan 05 2015 *)
LinearRecurrence[{4,-4,0,2},{0,0,1,3},30] (* Harvey P. Dale, Aug 05 2018 *)

G.f.: x^2*(1-x)/(1 - 4*x + 4*x^2 - 2*x^4).
a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-4).
a(n) = sum_{k=0..n} binomial(n, k) * A000129(k/2) * (1+(-1)^k)/2.

cp's OEIS Frontend

A135153 Repeat Pell numbers A000129.

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