A166471 a(n) = 2^L(n+1)*3^L(n), where L(n) is the n-th Lucas number (A000032(n)).

18, 24, 432, 10368, 4478976, 46438023168, 207994791256915968, 9658866935211987562213146624, 2008994011967745042140303999261186371230892032

Offset: 0

Author

Matthew Vandermast, Nov 05 2009, Nov 07 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..14

Crossrefs

Cf. A000032, A001612, A002110, A166469, A166470, A166472, A166473.

All terms but the first belong to A025487.

Subsequence of A003586.

Programs

Magma

[2^Lucas(n+1)*3^Lucas(n): n in [0..10]]; // G. C. Greubel, Jul 30 2024

Mathematica

Table[2^LucasL[n+1]*3^LucasL[n], {n,0,10}] (* G. C. Greubel, May 15 2016 *)

SageMath

def l(n): return lucas_number2(n,1,-1);
[2^l(n+1)*3^l(n) for n in range(11)] # G. C. Greubel, Jul 30 2024

Formula

a(n) = a(n-1)*a(n-2), for n > 1, with a(0) = 18, a(1) = 24.

For m>1, n>0, A166469(A002110(m)*(a(n)^k)/12) = k*Lucas(m+n).

A166469(a(n)) = Lucas(n+2) + 1 = A001612(n+2).