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A084130 a(n) = 8a(n-1)-8a(n-2), a(0)=1, a(1)=4. 7
1, 4, 24, 160, 1088, 7424, 50688, 346112, 2363392, 16138240, 110198784, 752484352, 5138284544, 35086401536, 239584935936, 1635988275200, 11171226714112, 76281907511296, 520885446377472, 3556828310929408, 24287542916415488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A001541.

Let A be the unit-primitive matrix (see [Jeffery]) A = A_(8,3) = [0,0,0,1; 0,0,2,0; 0,2,0,1; 2,0,2,0]. Then A084130(n) = (1/4)*Trace(A^(2*n)). (Cf. A006012, A001333.) - L. Edson Jeffery, Apr 04 2011

a(n) is also the rational part of the Q(sqrt*(2)) integer giving the length L(n) of a variant of the Lévy C-curve, given by _Kival Ngaokrajan_, at iteration step n. See A057084. - Wolfdieter Lang, Dec 18 2014

LINKS

Table of n, a(n) for n=0..20.

L. E. Jeffery, Unit-primitive matrices

Index entries for linear recurrences with constant coefficients, signature (8,-8)

FORMULA

a(n) = (4+sqrt(8))^n/2 + (4-sqrt(8))^n/2.

G.f.: (1-4x)/(1-8x+8x^2).

E.g.f.: exp(4x)cosh(sqrt(8)x).

a(n) = A057084(n)-4*A057084(n-1). - R. J. Mathar, Nov 10 2013

MATHEMATICA

LinearRecurrence[{8, -8}, {1, 4}, 30] (* Harvey P. Dale, Sep 25 2014 *)

PROG

(PARI) {a(n)= if(n<0, 0, real((4+ 2*quadgen(8))^n))}

CROSSREFS

Cf. A084131.

Sequence in context: A210474 A117337 A272865 * A059304 A069722 A027079

Adjacent sequences:  A084127 A084128 A084129 * A084131 A084132 A084133

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2003

STATUS

approved

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Last modified February 24 04:33 EST 2018. Contains 299595 sequences. (Running on oeis4.)