

A151688


G.f.: Prod_{ 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
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 Prod_{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



