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A133592 a(n)=2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8 . 2
1, 2, 8, 28, 104, 376, 1376, 5008, 18272, 66592, 242816, 885184, 3227264, 11765632, 42894848, 156383488, 570136064, 2078573056, 7577962496, 27627363328, 100722501632, 367209183232, 1338753376256, 4880761851904, 17794043961344 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (2,6).

FORMULA

G.f.: (1-2*x^2)/(1-2*x-6*x^2) . a(n) = Sum_{k, 0<=k<=n}A122950(n,k)*2^k .

a(n)=[1+sqrt(7)]^(n-1)+[1-sqrt(7)]^(n-1)-(3/7)*[1-sqrt(7)]^(n-1)*sqrt(7)+(3/7)*[1+sqrt(7)]^(n-1)*sqrt(7) +(1/3)*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Nov 18 2008]

((7+2*sqrt(7))/21)*(1+sqrt(7))^n+((7-2*sqrt(7))/21)*(1-sqrt(7))^n for n=>1 [From Richard Choulet, Nov 19 2008]

a(n) = A083099(n+1) - 2*A083099(n-1). - R. J. Mathar, Jun 20 2015

MAPLE

A133592 := proc(n)

        option remember;

        if n <=1 then

                n+1;

        elif n = 2 then

                8;

        else

                2*procname(n-1)+6*procname(n-2) ;

        fi ;

end proc: # R. J. Mathar, Jul 15 2017

CROSSREFS

Sequence in context: A104934 A056711 A114590 * A115967 A150714 A292668

Adjacent sequences:  A133589 A133590 A133591 * A133593 A133594 A133595

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Dec 31 2007

EXTENSIONS

a(16) corrected by R. J. Mathar, Jun 20 2015

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)