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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Each group can be formed into a triangle.
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FORMULA
| a(n) = (2n^5+15n^4+44n^3+69n^2+62n+24)/24.
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EXAMPLE
| (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
| 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
| Cf. A000217, A000292.
Sequence in context: A152996 A188351 A060008 * A126899 A162602 A008501
Adjacent sequences: A095163 A095164 A095165 * A095167 A095168 A095169
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2004
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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