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Search: id:A100791
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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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+0
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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The leading diagonal is A000292 (tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6.)
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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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CROSSREFS
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Cf. A100792.
Sequence in context: A094414 A107984 A133178 this_sequence A056883 A006747 A108412
Adjacent sequences: A100788 A100789 A100790 this_sequence A100792 A100793 A100794
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 01 2004
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 10 2004
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