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

0,4

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).

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

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 *)

Prog

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

Crossrefs

Cf. A006646, A002203.

Sequence in context: A232331 A231992 A292044 * A232494 A037530 A083320

Adjacent sequences: A006665 A006666 A006667 * A006669 A006670 A006671

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved