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A170842
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G.f.: Product_{k>=1} (1 + 2x^(2^k-1) + 3x^(2^k)).
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1
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1, 2, 3, 2, 7, 12, 9, 2, 7, 12, 13, 20, 45, 54, 27, 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81, 2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, 79, 150, 243, 224, 133, 150, 259, 344, 537, 936, 1161, 810, 243, 2, 7, 12, 13, 20, 45
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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From Omar E. Pol, Apr 10 2021: (Start)
It appears that this is also an irregular triangle read by rows (see the example).
It appears that right border gives A000244.
It appears that row sums give A052934. (End)
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LINKS
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Table of n, a(n) for n=0..68.
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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EXAMPLE
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From Omar E. Pol, Apr 10 2021: (Start)
Written as an irregular triangle in which row lengths are A000079 the sequence begins:
1;
2, 3;
2, 7, 12, 9;
2, 7, 12, 13, 20, 45, 54, 27;
2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 81;
2, 7, 12, 13, 20, 45, 54, 31, 20, 45, 62, 79, 150, 243, 216, 85, 20, 45, 62, ...
(End)
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MATHEMATICA
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CoefficientList[Series[Product[1+2x^(2^k-1)+3x^2^k, {k, 10}], {x, 0, 70}], x] (* Harvey P. Dale, Apr 09 2021 *)
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CROSSREFS
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Cf. A000079, A000244, A052934, A275667.
Sequence in context: A122076 A209774 A271322 * A014784 A048601 A008317
Adjacent sequences: A170839 A170840 A170841 * A170843 A170844 A170845
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Jan 02 2010
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STATUS
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approved
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