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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 08:16 EST 2021. Contains 349419 sequences. (Running on oeis4.)