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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also, first differences of toothpicks numbers A152998. [From Omar E. Pol (info(AT)polprimos.com), Jan 02 2009]
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LINKS
| 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
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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^r-1) = 2^(r-1). - N. J. A. Sloane, Jun 03 2009, Jul 16 2009
G.f.: x*(Prod(1+x^(2^k-1)+2*x^(2^k),k=0..oo)-1)/(1+2*x). - N. J. A. Sloane, Jun 05 2009
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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
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CROSSREFS
| Cf. A139250, A139251, A139252, A152978, A152980, A153006, A152998.
Sequence in context: A024405 A082547 A068928 * A086420 A170887 A103265
Adjacent sequences: A152965 A152966 A152967 * A152969 A152970 A152971
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 16 2008, Dec 20 2008
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