OFFSET
1,1
COMMENTS
Greedy summability is defined at A242288.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
Let s(n) = n(n+1)(n+2)/6 = A000292(n). Then
a(1) = 35 = 20 + 10 + 4 + 1;
a(2) = 56 = 35 + 20 + 1;
a(3) = 120 = 84 + 35 + 1;
a(4) = 165 = 120 + 35 + 10.
MATHEMATICA
z = 200; s = Table[n (n + 1)(n + 2)/6, {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}] (* A242288 *)
c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242289 *)
f = 1 + Flatten[Position[tr, 0]] (* A242290*)
f (f + 1)(f + 2)/6 (* A242291 *) (* Peter J. C. Moses, May 06 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 10 2014
STATUS
approved