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Search: id:A124287
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| A124287 |
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Triangle of the number of integer-sided k-gons having perimeter n, for k=3..n. |
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4
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| 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 3, 1, 1, 1, 5, 4, 4, 1, 1, 3, 7, 9, 7, 4, 1, 1, 2, 9, 13, 15, 8, 5, 1, 1, 4, 13, 23, 25, 20, 10, 5, 1, 1, 3, 16, 29, 46, 37, 29, 12, 6, 1, 1, 5, 22, 48, 72, 75, 57, 35, 14, 6, 1, 1, 4, 25, 60, 113, 129, 125, 79, 47, 16, 7, 1, 1, 7, 34, 92, 172, 228, 231, 185
(list; graph; listen)
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OFFSET
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3,8
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COMMENT
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Rotations and reversals are counted only once. For a k-gon to be nondegenerate, the longest side must be shorter than the sum of the remaining sides. Column k=3 is A005044, column k=4 is A057886, column k=5 is A124285 and column k=6 is A124286. Note that A124278 counts polygons whose sides are nondecreasing.
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LINKS
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T. D. Noe, Table of n, a(n) for n=3..212
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EXAMPLE
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For polygons having perimeter 7: 2 triangles, 3 quadrilaterals, 3 pentagons, 1 hexagon and 1 heptagon. The triangle begins
1
0 1
1 1 1
1 2 1 1
2 3 3 1 1
1 5 4 4 1 1
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Table[p=Partitions[n]; Table[s=Select[p, Length[ # ]==k && #[[1]]<Total[Rest[ # ]] &]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[k, s[[i]], Dihedral]], {i, Length[s]}]; cnt, {k, 3, n}], {n, 3, 20}]
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CROSSREFS
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Sequence in context: A087741 A054991 A047071 this_sequence A060240 A153734 A128495
Adjacent sequences: A124284 A124285 A124286 this_sequence A124288 A124289 A124290
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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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