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

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 (6,-4,-8).

Crossrefs

Cf. A000129, A002203, A006668.

Programs

Magma

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

Mathematica

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

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