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Search: id:A095166
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| A095166 |
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Group the natural numbers so that the n-th group contains n(n+1)/2 numbers and obtain the group sum. |
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+0
1
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| 1, 9, 45, 155, 420, 966, 1974, 3690, 6435, 10615, 16731, 25389, 37310, 53340, 74460, 101796, 136629, 180405, 234745, 301455, 382536, 480194, 596850, 735150, 897975, 1088451, 1309959, 1566145, 1860930, 2198520, 2583416, 3020424, 3514665
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Each group can be formed into a triangle.
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FORMULA
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a(n) = (2n^5+15n^4+44n^3+69n^2+62n+24)/24.
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EXAMPLE
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(1), (2, 3, 4), (5, 6, 7, 8, 9, 10), (11, 12, 13, 14, 15, 16, 17, 18, 19, 20), ...
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MATHEMATICA
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tetr[n_] := Binomial[n + 3, 3]; tri[n_] := (n(n + 1)/2); Table[ tri[ tetr[n]] - tri[ tetr[n - 1]], {n, 0, 32}] (from Robert G. Wilson v Jun 05 2004)
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CROSSREFS
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Cf. A000217, A000292.
Sequence in context: A139609 A068314 A060008 this_sequence A126899 A008501 A008491
Adjacent sequences: A095163 A095164 A095165 this_sequence A095167 A095168 A095169
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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