Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jan 01 2020 21:52:24
%S 1,5,4,18,17,10,50,48,37,20,115,110,93,67,35,231,220,194,156,109,56,
%T 420,399,360,306,240,165,84,708,672,615,540,450,348,237,120,1125,1068,
%U 987,885,765,630,483,327,165,1705,1620,1508,1372,1215,1040,850,648,437,220
%N 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.
%C The leading diagonal is A000292 (tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6.)
%C 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
%H Harvey P. Dale, <a href="/A100791/b100791.txt">Table of n, a(n) for n = 1..10000</a>
%e 1
%e 5 4
%e 18 17 10
%e 50 48 37 20
%e 115 110 93 67 35
%e ...
%t 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 *)
%Y Cf. A100792.
%K easy,nonn,tabl
%O 1,2
%A _Amarnath Murthy_, Dec 01 2004
%E More terms from _Ray Chandler_, Dec 10 2004