

A151688


G.f.: Product_{n>=0} (1 + x^(2^n1) + 2*x^(2^n)).


14



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
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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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)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^k1) + 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 A056942 A115947
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



