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%I #4 May 15 2014 10:16:14
%S 10,21,28,45,55,66,91,105,120,136,171,190,231,253,300,325,378,406,435,
%T 496,528,595,630,666,703,780,820,903,946,1035,1081,1176,1225,1326,
%U 1378,1485,1540,1596,1711,1770,1891,1953,2080,2145,2211,2278,2415,2485,2628
%N Greedy-summable triangular numbers.
%C Greedy summability is defined at A242284.
%H Clark Kimberling, <a href="/A242287/b242287.txt">Table of n, a(n) for n = 1..1000</a>
%e Let s(n) = n(n+1)/2 = A000217(n). Then
%e a(1) = 10 = 6 + 3 + 1;
%e a(2) = 21 = 15 + 6;
%e a(3) = 28 = 21 + 6 + 1;
%e a(4) = 45 = 36 + 6 + 3.
%t z = 200; s = Table[n (n + 1)/2, {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]
%t r[n_] := s[[n]] - Total[t[[n]][[2]]];
%t tr = Table[r[n], {n, 2, z}] (* A242284 *)
%t c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242285 *)
%t f = 1 + Flatten[Position[tr, 0]] (* A242286 *)
%t f (f + 1)/2 (* A242287 *) (* _Peter J. C. Moses_, May 06 2014 *)
%Y Cf. A242284, A242285, A242286, A241833, A000217.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 10 2014
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