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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-4,-8).
Programs
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Magma
[Floor(((2+Sqrt(8))^n+(2-Sqrt(8))^n-2^(n+1))/16): n in [0..30] ]; // Vincenzo Librandi, Aug 20 2011
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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
Comments