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A100791 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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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 10,000 terms, only 12 are duplicates and there are no terms that repeat more than two times. - Harvey P. Dale, Jun 10 2018

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000

EXAMPLE

1

5 4

18 17 10

50 48 37 20

115 110 93 67 35

...

MATHEMATICA

  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 *)

CROSSREFS

Cf. A100792.

Sequence in context: A282225 A282202 A190728 * A056883 A006747 A184297

Adjacent sequences:  A100788 A100789 A100790 * A100792 A100793 A100794

KEYWORD

easy,nonn,tabl

AUTHOR

Amarnath Murthy, Dec 01 2004

EXTENSIONS

More terms from Ray Chandler, Dec 10 2004

STATUS

approved

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Last modified February 23 18:13 EST 2019. Contains 320437 sequences. (Running on oeis4.)