A006646 Exponential self-convolution of Pell numbers.

0, 0, 2, 12, 64, 320, 1568, 7616, 36864, 178176, 860672, 4156416, 20070400, 96911360, 467935232, 2259402752, 10909384704, 52675215360, 254338531328, 1228055248896, 5929575645184, 28630524624896

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-4,-8).

Formula

a(n) = ((2+sqrt(8))^n+(2-sqrt(8))^n-2^(n+1))/8; E.g.f.: exp(2x)(sinh(sqrt(2)*x))^2/2 = (exp(x)*sinh(sqrt(2)*x)/sqrt(2))^2. - Paul Barry, May 16 2003

G.f.: 2*x^2 / ( (2*x-1)*(4*x^2+4*x-1) ). - R. J. Mathar, Nov 24 2012

a(n) = 2^(n-3)*(A002203(n) - 2). - Vladimir Reshetnikov, Oct 07 2016

Mathematica

Table[2^(n-3)*(LucasL[n, 2] - 2), {n, 0, 20}] (* Vladimir Reshetnikov, Oct 07 2016 *)

Prog

(Magma) [Floor(((2+Sqrt(8))^n+(2-Sqrt(8))^n-2^(n+1))/8): n in [0..30] ]; // Vincenzo Librandi, Aug 20 2011

Crossrefs

Cf. A000129, A002203, A006668.

Sequence in context: A368760 A272363 A283488 * A087635 A180038 A052896

Adjacent sequences: A006643 A006644 A006645 * A006647 A006648 A006649

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved