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Search: id:A124285
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| A124285 |
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Number of integer-sided pentagons having perimeter n. |
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+0
3
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| 0, 0, 0, 0, 1, 1, 3, 4, 9, 13, 23, 29, 48, 60, 92, 109, 158, 186, 258, 296, 397, 451, 589, 658, 841, 933, 1169, 1283, 1582, 1728, 2100, 2275, 2732, 2948, 3502, 3756, 4419, 4725, 5511, 5866, 6789, 7207, 8283, 8761, 10006, 10560, 11990, 12617, 14250, 14968
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Rotations and reversals are counted only once. Note that this is different from A069906, which counts pentagons whose sides are nondecreasing.
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EXAMPLE
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The three pentagons having perimeter 7 are (1,1,1,2,2), (1,1,2,1,2) and (1,1,1,1,3).
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==5 && #[[1]]<Total[Rest[ # ]]&]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[5, s[[i]], Dihedral]], {i, Length[s]}]; cnt, {n, 50}]
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CROSSREFS
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Cf. A057886 (quadrilaterals), A124286 (hexagons), A124287 (k-gons).
Sequence in context: A029448 A103014 A116552 this_sequence A131326 A089300 A079284
Adjacent sequences: A124282 A124283 A124284 this_sequence A124286 A124287 A124288
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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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