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Search: id:A057886
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| A057886 |
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Number of integer 4-tuples that give the lengths of the sides of a nongenerate quadrilateral with perimeter n. |
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5
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| 0, 0, 0, 1, 1, 2, 3, 5, 7, 9, 13, 16, 22, 25, 34, 38, 50, 54, 70, 75, 95, 100, 125, 131, 161, 167, 203, 210, 252, 259, 308, 316, 372, 380, 444, 453, 525, 534, 615, 625, 715, 725, 825, 836, 946, 957, 1078, 1090, 1222, 1234, 1378, 1391, 1547, 1560, 1729, 1743
(list; graph; listen)
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OFFSET
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1,6
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REFERENCES
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Related to: T. Jenkyns and E. Muller, Triangular triples from ceilings to floors, Amer. Math. Monthly, 107 (Aug. 2000), 634-639.
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FORMULA
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Conjecture: a(1)=0 and, for n>1, a(n)=a(n-1)+d(n-1), where d(n)=floor(n/4)*floor((n-2)/4) if n is even and d(n)=floor((n+1)/4) if n is odd.
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EXAMPLE
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There are five quadrilaterals with perimeter 8, with sides (1,1,3,3), (1,2,2,3), (1,2,3,2), (1,3,1,3) and (2,2,2,2), so a(8)=5.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==4 && #[[1]]<Total[Rest[ # ]] &]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[4, s[[i]], Dihedral]], {i, Length[s]}]; cnt, {n, 50}] - T. D. Noe (noe(AT)sspectra.com), Oct 24 2006
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CROSSREFS
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The Moebius transform is A057887. Cf. A005044.
Cf. A062890.
Sequence in context: A080000 A032459 A028870 this_sequence A069999 A035563 A028378
Adjacent sequences: A057883 A057884 A057885 this_sequence A057887 A057888 A057889
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Sep 19 2000
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EXTENSIONS
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Corrected by T. D. Noe, Oct 24 2006
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