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A100791
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Group the natural numbers so that the n-th group contains n(n+1)/2 = T(n) terms: (1), (2,3,4), (5,6,7,8,9,10), (11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35),... The n-th row of the following triangle is formed from the sum of first n terms, next n-1 terms,next n-2 terms ... of the n-th group; e.g. third row is (5+6+7), (8+9), (10) or 18,17,10. Sequence contains the triangle read by rows.
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2
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1, 5, 4, 18, 17, 10, 50, 48, 37, 20, 115, 110, 93, 67, 35, 231, 220, 194, 156, 109, 56, 420, 399, 360, 306, 240, 165, 84, 708, 672, 615, 540, 450, 348, 237, 120, 1125, 1068, 987, 885, 765, 630, 483, 327, 165, 1705, 1620, 1508, 1372, 1215, 1040, 850, 648, 437, 220
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OFFSET
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1,2
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COMMENTS
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The leading diagonal is A000292 (tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6.)
The sequence contains very few duplicate terms. In the first 10000 terms, only 12 are duplicates and there are no terms that repeat more than two times. - Harvey P. Dale, Jun 10 2018
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LINKS
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EXAMPLE
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1
5 4
18 17 10
50 48 37 20
115 110 93 67 35
...
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MATHEMATICA
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Module[{nn=10, r1, r2}, r1=Accumulate[Range[nn]]; r2=Total[r1]; Total/@ Flatten[ TakeList[#, Range[(Sqrt[8*Length[#]+1]-1)/2, 1, -1]]&/@TakeList[ Range[ r2], r1], 1]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jun 10 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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