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A242287
Greedy-summable triangular numbers.
4
10, 21, 28, 45, 55, 66, 91, 105, 120, 136, 171, 190, 231, 253, 300, 325, 378, 406, 435, 496, 528, 595, 630, 666, 703, 780, 820, 903, 946, 1035, 1081, 1176, 1225, 1326, 1378, 1485, 1540, 1596, 1711, 1770, 1891, 1953, 2080, 2145, 2211, 2278, 2415, 2485, 2628
OFFSET
1,1
COMMENTS
Greedy summability is defined at A242284.
LINKS
EXAMPLE
Let s(n) = n(n+1)/2 = A000217(n). Then
a(1) = 10 = 6 + 3 + 1;
a(2) = 21 = 15 + 6;
a(3) = 28 = 21 + 6 + 1;
a(4) = 45 = 36 + 6 + 3.
MATHEMATICA
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}]
r[n_] := s[[n]] - Total[t[[n]][[2]]];
tr = Table[r[n], {n, 2, z}] (* A242284 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242285 *)
f = 1 + Flatten[Position[tr, 0]] (* A242286 *)
f (f + 1)/2 (* A242287 *) (* Peter J. C. Moses, May 06 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 10 2014
STATUS
approved