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Search: id:A108416
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| A108416 |
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Triangle read by rows: T(n,k) counts the k-subsets of the n-th roots of 1 with absolute value of sum=1. |
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+0
2
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| 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 0, 5, 0, 0, 6, 6, 12, 0, 7, 0, 0, 0, 8, 0, 24, 0, 0, 9, 9, 0, 18, 0, 10, 0, 40, 10, 60, 0, 11, 0, 0, 0, 0, 0, 12, 12, 60, 72, 144, 120, 0, 13, 0, 0, 0, 0, 0, 0, 14, 0, 84, 0, 210, 14, 280, 0, 15, 15, 0, 75, 60, 30, 105, 0, 16, 0, 112, 0, 336, 0, 560, 0, 0, 17, 0, 0
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row n is divisible by n (rotation symmetry). Table starts 0, 0,1, 0,2,0, 0,3,3,0, 0,4,0,4,0, 0,5,0,0,5,0, 0,6,6,12,6,6,0, 0,7,0,0,0,0,7,0, 0,8,0,24,0,24,0,8,0, 0,9,9,0,18,18,0,9,9,0 row sums=A108417.
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EXAMPLE
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T(6,2)=6, counting {1,3}, {1,5}, {2,4}, {2,6}, {3,5}, {4,6}.
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MATHEMATICA
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<<DiscreteMath`Combinatorica`; Table[Count[KSubsets[Range[n], k], q_List/; Chop[ -1+Abs[Plus @@ (E^((2.*Pi*I*q)/n))]] === 0], {n, 16}, {k, 0, n}]
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CROSSREFS
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Cf. A107754, A103314, A108417.
Sequence in context: A029220 A137303 A049084 this_sequence A108760 A137304 A027656
Adjacent sequences: A108413 A108414 A108415 this_sequence A108417 A108418 A108419
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 02 2005
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