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Search: id:A088803
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| A088803 |
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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 every pile with more than 1 token is divided into two and half the token are added to the pile on the left and half to the pile on the right. If a pile has an odd number of tokens, the token left over stays where it is. The redistributions in each step are done in parallel. |
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+0
2
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| 1, 3, 7, 11, 17, 25, 33, 41, 53, 65, 77, 93, 109, 123, 143, 163, 181, 203, 227, 249, 277, 303, 329, 357, 389, 417, 451, 485, 517, 555, 593, 629, 669, 711, 749, 795, 839, 883, 931, 981, 1025, 1077, 1131, 1179, 1235, 1293, 1343, 1403, 1465, 1519, 1583, 1649
(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.
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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 0.65, with estimate 0.5973 for n = 10, 000.
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EXAMPLE
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E.g. a(2) = 3 because there are 3 steps in the process beginning with 4 tokens:
0 0 4 0 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. A088804.
Sequence in context: A134707 A047838 A029715 this_sequence A088206 A052341 A038949
Adjacent sequences: A088800 A088801 A088802 this_sequence A088804 A088805 A088806
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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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