A151692 G.f.: Product_{k>=2} (1 + x^(2^k-1) + x^(2^k)).

1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 1, 3, 3, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 1, 3, 3, 1, 0, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 2, 4, 6, 4, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 1, 3, 3, 1, 0, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 2, 4, 6, 4, 1, 0, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 2

Offset: 0

Author

N. J. A. Sloane, Jun 04 2009

Keywords

• nonn

Examples

			From _Omar E. Pol_, Jun 09 2009: (Start)
Triangle begins:
  1;
  0,0;
  1,1,0,0;
  1,1,0,1,2,1,0,0;
  1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,0;
  1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,0;
  1,1,0,1,2,1,0,1,2,1,1,3,3,1,0,1,2,1,1,3,3,1,1,3,3,2,4,6,4,1,0,1,2,1,1,3,3,...
(End)
		

Links

• 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

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. A160573, A151552.

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