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.

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

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 10000 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: A282202 A190728 A344435 * 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