A081017 a(n) = Lucas(4n+1) - 1, or 5*Fibonacci(2n)*Fibonacci(2n+1).

0, 10, 75, 520, 3570, 24475, 167760, 1149850, 7881195, 54018520, 370248450, 2537720635, 17393796000, 119218851370, 817138163595, 5600748293800, 38388099893010, 263115950957275, 1803423556807920, 12360848946698170

Offset: 0

Author

R. K. Guy, Mar 01 2003

Keywords

• nonn
• easy

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Crossrefs

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

Programs

GAP

List([0..20], n-> Lucas(1,-1, 4*n+1)[2] -1 ); # G. C. Greubel, Jul 14 2019

Magma

[Lucas(4*n+1) -1: n in [0..20]]; // G. C. Greubel, Jul 14 2019

Maple

with(combinat): 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 25 do printf(`%d,`,luc(4*n+1)-1) od: # James Sellers, Mar 03 2003

Mathematica

LucasL[4*Range[0,20]+1]-1 (* or *) LinearRecurrence[{8,-8,1},{0,10,75},20] (* Harvey P. Dale, Mar 02 2015 *)

PARI

vector(20, n, n--; f=fibonacci; f(4*n+2)+f(4*n)-1) \\ G. C. Greubel, Jul 14 2019

Sage

[lucas_number2(4*n+1, 1,-1) - 1 for n in (0..20)] # G. C. Greubel, Jul 14 2019

Formula

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

G.f.: 5*x*(2-x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Apr 16 2012

Extensions

More terms from James Sellers, Mar 03 2003