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A006668
Exponential self-convolution of Pell numbers (divided by 2).
4
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
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
Sequence in context: A232331 A231992 A292044 * A232494 A037530 A083320
KEYWORD
nonn,easy
AUTHOR
STATUS
approved