A151688 G.f.: Product_{n>=0} (1 + x^(2^n-1) + 2*x^(2^n)).

2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 18, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 96, 34, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 98, 44, 30, 46, 56, 70, 104, 130, 112, 86, 106, 148, 182, 244, 336, 352, 224, 66, 8, 14, 18, 20, 30, 44

Offset

0,1

Comments

This is essentially the same g.f. as A151550 but with the n=0 term included.

Links

Table of n, a(n) for n=0..69.

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

Formula

a(n) = Sum_{k>=0} 2^(wt(n+k)-k)*binomial(wt(n+k),k).

Example

If written as a triangle, begins:
  2;
  4;
  6, 6;
  8, 14, 16, 10;
  8, 14, 18, 20, 30, 44, 40, 18;
  8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 96, 34;
  ...

Crossrefs

Equals 2*A152980 = A147646/2.

Equals limit of rows of triangle in A152968.

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. A151550, A139251, A139250.

Sequence in context: A023853 A056526 A049066 * A159276 A359362 A056942

Adjacent sequences: A151685 A151686 A151687 * A151689 A151690 A151691

Keyword

nonn,tabf

Author

Omar E. Pol, May 02 2009

Extensions

Edited by N. J. A. Sloane, Jun 03 2009, Jul 14 2009

Status

approved