A081070 Lucas(4n)-2, or 5*Fibonacci(2n)^2.

0, 5, 45, 320, 2205, 15125, 103680, 710645, 4870845, 33385280, 228826125, 1568397605, 10749957120, 73681302245, 505019158605, 3461452808000, 23725150497405, 162614600673845, 1114577054219520, 7639424778862805

Offset: 0

Author

R. K. Guy, Mar 04 2003

Keywords

• nonn
• easy

References

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

Links

• 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).

Crossrefs

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

Programs

Magma

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

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 Sellers, Mar 05 2003

Mathematica

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

PARI

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

Formula

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

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

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