A151694 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + 2*x^(2^k)).

1, 2, 2, 2, 6, 8, 4, 2, 6, 8, 8, 16, 28, 24, 8, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88, 104, 64, 16, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88, 104, 64, 20, 16, 28, 32, 48, 88, 104, 72, 56, 88, 120, 160, 272, 384, 336, 160, 32, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88

Offset

0,2

Links

Table of n, a(n) for n=0..75.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Example

From Omar E. Pol, Jun 09 2009: (Start)
Triangle begins:
  1;
  2,2;
  2,6,8,4;
  2,6,8,8,16,28,24,8;
  2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,16;
  2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,20,16,28,32,48,88,104,72,56,88,...
(End)

Mathematica

CoefficientList[Series[Product[1+2x^(2^k-1)+2x^2^k, {k, 10}], {x, 0, 80}], x] (* Harvey P. Dale, Oct 07 2020 *)

Crossrefs

For generating functions of the form Product_{k>=c} (1 + a*x^(2^k-1) + b*x^2^k) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694.

Cf. A000079. - Omar E. Pol, Jun 09 2009

Sequence in context: A081478 A105341 A194676 * A361424 A298745 A323860

Adjacent sequences: A151691 A151692 A151693 * A151695 A151696 A151697

Keyword

nonn

Author

N. J. A. Sloane, Jun 04 2009

Status

approved