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(n^3)-th Lucas number (beginning at 2).
1

%I #11 Jul 07 2012 20:44:44

%S 2,1,47,439204,23725150497407,132878596168524201724674011,

%T 1384619022984618483717737087933569992335566082,

%U 481682208844384447843365760878364816732549453120338354329505085763436029

%N (n^3)-th Lucas number (beginning at 2).

%C This is to A182149 (n^3)-th Fibonacci number, as A000032 is to A000045.

%H Alois P. Heinz, <a href="/A214221/b214221.txt">Table of n, a(n) for n = 0..16</a>

%F a(n) = A000032(A000578(n)).

%F a(n) = term (1,1) in the 2 X 1 matrix [0,1; 1,1]^(n^3) * [2;1]. - _Alois P. Heinz_, Jul 07 2012

%e a(2) = L(2^3) = L(8) = 47.

%p a:= n-> (<<0|1>, <1|1>>^(n^3). <<2, 1>>)[1, 1]:

%p seq (a(n), n=0..7); # _Alois P. Heinz_, Jul 07 2012

%t f[n_] := LucasL[n^3]; Array[f, 8, 0] (* _Robert G. Wilson v_, Jul 07 2012 *)

%Y Cf. A000032, A000045, A000578, A166169, A182149.

%K nonn,easy

%O 0,1

%A _Jonathan Vos Post_, Jul 07 2012