



1, 2, 2, 2, 4, 6, 4, 2, 4, 6, 6, 8, 14, 16, 8, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 16, 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, 32, 2
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OFFSET

1,2


COMMENTS

Also, first differences of toothpicks numbers A152998. [From Omar E. Pol, Jan 02 2009]


LINKS

Table of n, a(n) for n=1..64.
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

Write n = 2^i +j, 0 <= j < 2^i; then a(n) = Sum_k 2^(wt(j+k)k)*binomial(wt(j+k),k). except that a(2^r1) = 2^(r1).  N. J. A. Sloane, Jun 03 2009, Jul 16 2009
G.f.: x*(Prod(1+x^(2^k1)+2*x^(2^k),k=0..oo)1)/(1+2*x).  N. J. A. Sloane, Jun 05 2009


EXAMPLE

Triangle begins:
.1;
.2,2;
.2,4,6,4;
.2,4,6,6,8,14,16,8;
.2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,16;
....
Rows approach A151688.  N. J. A. Sloane, Jun 03 2009


CROSSREFS

Cf. A139250, A139251, A139252, A152978, A152980, A153006, A152998.
Sequence in context: A278502 A278501 A278231 * A222177 A240433 A217637
Adjacent sequences: A152965 A152966 A152967 * A152969 A152970 A152971


KEYWORD

nonn


AUTHOR

Omar E. Pol, Dec 16 2008, Dec 20 2008


STATUS

approved



