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Search: id:A088804
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| A088804 |
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a(n) gives the number of steps taken in a process which manipulates piles of tokens arranged in a line. There are 2n (or 2n+1) tokens in all. Initially they are all in one pile. At each step, from each pile with more than 1 token, one token is taken and added to the pile on its left and one is taken and added to the pile on its right. The redistributions in each step are done in parallel. |
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+0
2
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| 1, 4, 8, 14, 21, 29, 39, 51, 63, 77, 93, 110, 128, 148, 170, 192, 216, 242, 268, 296, 326, 358, 390, 424, 460, 496, 534, 574, 615, 657, 701, 747, 793, 841, 891, 941, 993, 1047, 1103, 1159, 1217, 1277, 1337, 1399, 1463, 1529, 1595, 1663, 1733, 1803, 1875, 1949
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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R. Anderson, L. Lovasz, P. Shor, J. Spencer, E. Tardos, S. Winograd, Disks, balls and walls: analysis of a combinatorial game, Amer. Math. Monthly, 6, 96, pp. 481-493, 1989.
A Bjoerner, L Lovasz, PW Shor Chip-firing games on graphs European Journal of Combinatorics 12, pp. 283-291, 1991.
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LINKS
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Mikkel Thorup. Firing Games
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FORMULA
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The sequence is asymptotically quadratic with a(n) ~= c*n^2, where c is between 0.33 and 1, with estimate 0.7078 for n = 1, 000.
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EXAMPLE
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E.g. a(2) = 4 because there are 4 steps in the process beginning with 4 tokens:
0 0 4 0 0
0 1 2 1 0
0 2 0 2 0
1 0 2 0 1
1 1 0 1 1
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CROSSREFS
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Cf. A088803.
Sequence in context: A055507 A121896 A131937 this_sequence A027924 A006578 A122224
Adjacent sequences: A088801 A088802 A088803 this_sequence A088805 A088806 A088807
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KEYWORD
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nonn
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AUTHOR
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Rob Arthan (rda(AT)lemma-one.com), Oct 17 2003
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