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Search: id:A118888
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| A118888 |
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Number of ways to place n objects with weights 1,2,...,n evenly spaced around the circumference of a circular disk such that the remaining imbalance is minimized. |
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+0
2
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| 1, 1, 1, 1, 1, 2, 1, 2, 3, 24, 1, 732, 1, 720, 48, 144, 1
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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The position of weight 1 is kept fixed at position 1. Mirror configurations are counted only once. For n not a prime power, the sequence equals A118887.
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EXAMPLE
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a(5)=1: The configuration minimizing the remaining imbalance with respect to the center of the circle is [1 4 3 2 5] (and its mirror image).
Examples of minimum imbalance configurations not in A118887:
a(7)=1: [1 4 7 2 3 5 6];
a(8)=2: [1 4 7 3 6 2 5 8], [1 7 4 3 6 5 2 8];
a(9)=3: [1 5 9 2 7 3 4 8 6], [1 5 9 4 2 6 7 3 8], [1 6 5 4 9 2 3 7 8];
a(11)=1: [1 8 9 5 2 6 10 7 3 4 11];
a(13)=1: [1 2 7 12 13 4 5 3 8 6 11 9 10];
a(16)=144: lexicographically first [1 3 5 13 16 7 10 2 14 4 6 9 12 8 11 15];
a(17)=1: [1 7 3 17 10 9 15 2 14 6 5 4 16 8 13 12 11].
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CROSSREFS
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Cf. A118887.
Sequence in context: A086880 A120405 A034952 this_sequence A061678 A131022 A137408
Adjacent sequences: A118885 A118886 A118887 this_sequence A118889 A118890 A118891
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KEYWORD
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hard,more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), May 26 2006
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