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A160573
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G.f.: Prod_{ k >= 0} (1 + x^(2^k-1) + x^(2^k)).
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15
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2, 3, 3, 3, 5, 6, 4, 3, 5, 6, 6, 8, 11, 10, 5, 3, 5, 6, 6, 8, 11, 10, 7, 8, 11, 12, 14, 19, 21, 15, 6, 3, 5, 6, 6, 8, 11, 10, 7, 8, 11, 12, 14, 19, 21, 15, 8, 8, 11, 12, 14, 19, 21, 17, 15, 19, 23, 26, 33, 40, 36, 21, 7, 3, 5, 6, 6, 8, 11, 10, 7, 8, 11, 12, 14, 19, 21, 15, 8, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sequence mentioned in the Applegate-Pol-Sloane article, see chapter 9 "explicit formulas". - Omar E. Pol, Sep 20 2011
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REFERENCES
| D. Applegate, O. E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191
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LINKS
| David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, which is also available at arXiv:1004.3036v2
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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FORMULA
| a(n) = sum_{i >= 0} binomial(A000120(n+i),i)
For k >= 1, a(2^k-2) = k+1 and a(2^k-1) = 3; otherwise if n = 2^i + j, 0 <= j <= 2^i-3, a(n) = a(j) + a(j+1).
a(n) = 2*A151552(n) + A151552(n-1).
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EXAMPLE
| a(5) = binomial(2,0) + binomial(2,1) + binomial(3,2) + binomial(1,3) + binomial(2,4) + binomial(2,5) + ... = 1 + 2 + 3 + 0 + 0 + 0 + ... = 6
Contribution from Omar E. Pol, Jun 09 2009: (Start)
Triangle begins:
2;
3;3;
3,5,6,4;
3,5,6,6,8,11,10,5;
3,5,6,6,8,11,10,7,8,11,12,14,19,21,15,6;
3,5,6,6,8,11,10,7,8,11,12,14,19,21,15,8,8,11,12,14,19,21,17,15,19,23,26,...
(End)
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MAPLE
| See A118977 for Maple code.
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CROSSREFS
| For generating functions of the form Prod_{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
Row sums of A151683. See A151687 for another version.
Cf. A151552 (G.f. has one factor fewer)
Limiting form of rows of A118977 when that sequence is written as a triangle and the initial 1 is omitted. - N. J. A. Sloane, Jun 01 2009.
Cf. A139250, A139251. - Omar E. Pol, Sep 20 2011
Sequence in context: A014202 A145281 A151687 * A141418 A130499 A020910
Adjacent sequences: A160570 A160571 A160572 * A160574 A160575 A160576
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KEYWORD
| nonn
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AUTHOR
| Hagen von Eitzen, math(AT)von-eitzen.de, May 20 2009
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