A242287 Greedy-summable triangular numbers.

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

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

Cf. A242284, A242285, A242286, A241833, A000217.

Sequence in context: A087597 A087598 A363222 * A165403 A097386 A108685

Adjacent sequences: A242284 A242285 A242286 * A242288 A242289 A242290

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved