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A163311
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Triangle, diagonals = the infinite set of Toothpick sequences
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2
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1, 1, 2, 1, 3, 4, 1, 4, 7, 5, 1, 5, 10, 11, 7, 1, 6, 13, 19, 15, 10, 1, 7, 16, 29, 25, 23, 13, 1, 8, 19, 41, 37, 40, 35, 14, 1, 9, 22, 55, 51, 61, 67, 43, 16, 1, 10, 25, 71, 67, 86, 109, 94, 47, 19, 1, 11, 28, 89, 85, 115, 161, 173, 100, 55, 22, 1, 12, 31, 109, 105, 148, 223, 286, 181
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OFFSET
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1,3
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COMMENTS
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Row sums = A163312: (1, 3, 8, 17, 34, 64,...). Right border = A163267, Toothpick sequence for N=1. Next diagonal going to
the left = A139250, Toothpick sequence for N=2. Then 1, 4, 10, 19,... =
A162958, Toothpick sequence for N=3.
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LINKS
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Table of n, a(n) for n=1..75.
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
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(Cf. A162958 for rules governing the generation of N-th Toothpick sequences
By way of example, (N+2), A139250. The generator is A160552, which uses
the multiplier "2". Then A160552 convolved with (1, 2, 2, 2,...) = A139250
the Toothpick sequence for N=2. Similarly, we create an array for Toothpick
sequences N=1, 2, 3,...etc = A163267, A139250, A162958,...; then take the
antidiagonals, creating triangle A163311
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EXAMPLE
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First few rows of the triangle =
1;
1, 2;
1, 3, 4;
1, 4, 7, 5;
1, 5, 10, 11, 7;
1, 6, 13, 19, 15, 10;
1, 7, 16, 29, 25, 23, 13;
1, 8, 19, 41, 37, 40, 35, 14;
1, 9, 22, 55 51, 61, 67, 43, 16;
1, 10, 25, 71, 67, 86, 109, 94, 47, 19;
1, 11, 28, 89, 85, 115, 161, 173, 100, 55, 22;
1, 12, 31, 109, 105, 148, 223, 286, 181, 115, 67, 25;
1, 13, 34, 131, 127, 185, 295, 439, 296, 205, 142, 79, 30;
1, 14, 37, 155, 151, 226, 377, 638, 451, 331, 253, 175, 95, 36;
...
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CROSSREFS
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A163267, A139250, A162958, A160552
Sequence in context: A174829 A132110 A039912 * A210555 A008949 A076832
Adjacent sequences: A163308 A163309 A163310 * A163312 A163313 A163314
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Jul 24 2009
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STATUS
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approved
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