A006668 Exponential self-convolution of Pell numbers (divided by 2).

0, 0, 1, 6, 32, 160, 784, 3808, 18432, 89088, 430336, 2078208, 10035200, 48455680, 233967616, 1129701376, 5454692352, 26337607680, 127169265664, 614027624448, 2964787822592, 14315262312448, 69120201588736

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Binomial transform of A084150. - Paul Barry, May 16 2003

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. A006646, A002203.

Programs

Magma

[Floor(((2+Sqrt(8))^n+(2-Sqrt(8))^n-2^(n+1))/16): n in [0..30] ]; // Vincenzo Librandi, Aug 20 2011

Mathematica

LinearRecurrence[{6,-4,-8},{0,0,1},30] (* Harvey P. Dale, Jul 15 2014 *)
Table[2^(n-4)*(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))/16; E.g.f. : exp(2x)(sinh(sqrt(2)x))^2/4=(exp(x)sinh(sqrt(2)x)/sqrt(2))^2/2. - Paul Barry, May 16 2003

G.f.: x^2/((1-2*x)*(1-4*x-4*x^2)). - Bruno Berselli, Aug 20 2011

a(n) = A006646(n)/2 = 2^(n-4)*(A002203(n) - 2). - Vladimir Reshetnikov, Oct 07 2016