A055463 a(n) = 2*a(n-1)*a(n-2) - 3*a(n-3), with a(0) = 0, a(1) = 1, a(2) = 2.

0, 1, 2, 4, 13, 98, 2536, 497017, 2520869930, 2505830419990012, 12633745110864184300787269, 63316045634407119326463714272245870904666, 1599837563945889048330164752080268110156603845860584259478831024272

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..17

Formula

a(3*n+1) == 1 (mod 12), a(3*n+2) == 2 (mod 12), a(3*n+3) == 4 (mod 12). - Robert Israel, Jan 18 2018

Maple

A[0]:= 0: A[1]:= 1: A[2]:= 2:
for n from 3 to 17 do A[n]:= 2*A[n-1]*A[n-2]-3*A[n-3] od:
seq(A[i], i=0..17); # Robert Israel, Jan 18 2018

Mathematica

a[n_]:= a[n]= If[n<3, n, 2*a[n-1]*a[n-2] -3*a[n-3]];
Table[a[n], {n, 0, 15}] (* G. C. Greubel, Jan 31 2024 *)
nxt[{a_, b_, c_}]:={b, c, 2b*c-3a}; NestList[nxt, {0, 1, 2}, 20][[;; , 1]] (* Harvey P. Dale, Aug 16 2024 *)

Prog

(Magma)
function a(n) // a = A055463
  if n le 2 then return n;
  else return 2*a(n-1)*a(n-2) - 3*a(n-3);
  end if;
end function;
[a(n): n in [0..15]]; // G. C. Greubel, Jan 31 2024
(SageMath)
def a(n): # a = A055463
    if (n<3): return n
    else: return 2*a(n-1)*a(n-2) - 3*a(n-3)
[a(n) for n in range(16)] # G. C. Greubel, Jan 31 2024

Crossrefs

Sequence in context: A306445 A216670 A103845 * A369313 A091957 A327443

Adjacent sequences: A055460 A055461 A055462 * A055464 A055465 A055466

Keyword

easy,nonn

Author

Robert G. Wilson v, Jul 05 2000

Status

approved