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A110769 The r-th term of the n-th row of the following triangle contains sum of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 3 6 9 6 10 17 18 10 15 27 33 30 15 ... Sequence contains the triangle by rows. 4

%I #9 Jul 08 2018 13:40:50

%S 1,3,3,6,9,6,10,17,18,10,15,27,33,30,15,21,39,51,54,45,21,28,53,72,82,

%T 80,63,28,36,69,96,114,120,111,84,36,45,87,123,150,165,165,147,108,45,

%U 55,107,153,190,215,225,217,188,135,55,66,129,186,234,270,291,294,276

%N The r-th term of the n-th row of the following triangle contains sum of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 3 6 9 6 10 17 18 10 15 27 33 30 15 ... Sequence contains the triangle by rows.

%C The first term in the n-th row is T(n) and the n-th term also is T(n). - _Joshua Zucker_, Dec 14 2005

%H Harvey P. Dale, <a href="/A110769/b110769.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 4 the terms of the 4th row are 10, 9+8, 7+6+5, 4+3+2+1.

%t Table[Total/@TakeList[Range[(n(n+1))/2,1,-1],Range[n]],{n,20}]//Flatten (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, Jul 08 2018 *)

%Y Cf. A110768.

%K easy,tabl,nonn

%O 1,2

%A _Amarnath Murthy_, Aug 12 2005

%E Corrected and extended by _Joshua Zucker_, Dec 14 2005

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)