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Search: id:A124286
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| A124286 |
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Number of integer-sided hexagons having perimeter n. |
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+0
3
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| 0, 0, 0, 0, 0, 1, 1, 4, 7, 15, 25, 46, 72, 113, 172, 248, 360, 491, 686, 896, 1217, 1536, 2031, 2504, 3236, 3905, 4955, 5880, 7336, 8586, 10556, 12208, 14823, 16964, 20364, 23106, 27456, 30906, 36399, 40692, 47532, 52816, 61237, 67672, 77941, 85701
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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Rotations and reversals are counted only once. Note that this is different from A069907, which counts hexagons whose sides are nondecreasing.
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EXAMPLE
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The four hexagons having perimeter 8 are (1,1,1,1,2,2), (1,1,1,2,1,2), (1,1,2,1,1,2) and (1,1,1,1,1,3).
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==6 && #[[1]]<Total[Rest[ # ]]&]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[6, s[[i]], Dihedral]], {i, Length[s]}]; cnt, {n, 50}]
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CROSSREFS
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Cf. A057886 (quadrilaterals), A124285 (pentagons), A124287 (k-gons).
Sequence in context: A092309 A039669 A109622 this_sequence A027419 A116969 A131090
Adjacent sequences: A124283 A124284 A124285 this_sequence A124287 A124288 A124289
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Oct 24 2006
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