

A100791


Group the natural numbers so that the nth 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 nth row of the following triangle is formed from the sum of first n terms, next n1 terms,next n2 terms ... of the nth 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
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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



