login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 03:51 EST 2022. Contains 358362 sequences. (Running on oeis4.)