A166473 a(n) = 2^L(n+1) * 3^L(n)/12, where L(n) is the n-th Lucas number (A000032(n)).

2, 36, 864, 373248, 3869835264, 17332899271409664, 804905577934332296851095552, 167416167663978753511691999938432197602574336

Offset: 1

Author

Matthew Vandermast, Nov 05 2009

Keywords

• nonn

Comments

For m>1, A166469(A002110(m)*a(n)) = L(m+n).

A166469(a(n)) = L(n+2) - 2 = A014739(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..14

Crossrefs

Subsequence of A003586, A025487.

Programs

GAP

List([1..10], n-> 2^(Lucas(1,-1,n+1)[2]-2)*3^(Lucas(1,-1,n)[2]-1)); # G. C. Greubel, Jul 22 2019

Magma

[2^(Lucas(n+1)-2)*3^(Lucas(n)-1): n in [1..10]]; // G. C. Greubel, Jul 22 2019

Mathematica

Table[(2^LucasL[n+1] 3^LucasL[n])/12,{n,10}] (* Harvey P. Dale, Aug 17 2011 *)

PARI

lucas(n) = fibonacci(n+1) + fibonacci(n-1);
vector(10, n,  2^(lucas(n+1)-2)*3^(lucas(n)-1) ) \\ G. C. Greubel, Jul 22 2019

Sage

[2^(lucas_number2(n+1,1,-1)-2)*3^(lucas_number2(n,1,-1)-1) for n in (1..10)] # G. C. Greubel, Jul 22 2019

Formula

a(n) = A166471(n)/12.

For n>1, a(n) = 12*a(n-1) * a(n-2).