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A081070 Lucas(4n)-2, or 5*Fibonacci(2n)^2. 3
0, 5, 45, 320, 2205, 15125, 103680, 710645, 4870845, 33385280, 228826125, 1568397605, 10749957120, 73681302245, 505019158605, 3461452808000, 23725150497405, 162614600673845, 1114577054219520, 7639424778862805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

LINKS

Table of n, a(n) for n=0..19.

Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, arXiv:1111.5626 [cond-mat.dis-nn], 2011-2012 (see Eq. 4).

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

FORMULA

a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).

a(n) = 5*A049684(n).

a(n) = -2+[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n, with n>=0. - Paolo P. Lava, Dec 01 2008

G.f.: 5*x*(x+1)/((1-x)*(x^2-7*x+1)). - Colin Barker, Jun 24 2012

MAPLE

luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 40 do printf(`%d, `, luc(4*n)-2) od: # James A. Sellers, Mar 05 2003

MATHEMATICA

LinearRecurrence[{8, -8, 1}, {0, 5, 45}, 20] (* Jean-Fran├žois Alcover, Nov 24 2017 *)

PROG

(MAGMA) [Lucas(4*n)-2: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011

(PARI) a(n) = 5*fibonacci(2*n)^2; \\ Michel Marcus, Nov 24 2017

CROSSREFS

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A049684.

Sequence in context: A249638 A188349 A241275 * A247494 A043025 A190540

Adjacent sequences:  A081067 A081068 A081069 * A081071 A081072 A081073

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 04 2003

STATUS

approved

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Last modified February 18 02:09 EST 2018. Contains 299297 sequences. (Running on oeis4.)