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A242289
Number of terms in the greedy sum for the n-th tetrahedral number.
4
1, 2, 3, 4, 3, 4, 3, 3, 3, 3, 4, 4, 4, 2, 5, 5, 4, 5, 4, 4, 5, 3, 4, 4, 5, 4, 5, 6, 3, 5, 6, 3, 3, 5, 5, 4, 5, 6, 3, 4, 4, 4, 4, 4, 6, 5, 4, 4, 6, 5, 5, 6, 4, 2, 3, 6, 5, 4, 4, 3, 6, 6, 3, 4, 5, 6, 5, 6, 4, 5, 5, 6, 4, 5, 3, 5, 5, 6, 6, 4, 5, 5, 5, 3, 4, 5
OFFSET
2,2
COMMENTS
Greedy residues and related numbers are defined at A242288.
LINKS
EXAMPLE
n ... n(n+1)(n+2)/6 ... greedy sum
1 ... 1 ............... (undefined)
2 ... 4 ............... 1 = 1
3 ... 10 .............. 5 = 4 + 1
4 ... 20 .............. 15 = 10 + 4 + 1
5 ... 35 .............. 35 = 20 + 10 + 4 + 1
6 ... 56 .............. 56 = 35 + 20 + 1
7 ... 84 .............. 84 = 56 + 20 + 4 + 1
8 ... 120 ............. 120 = 84 + 35 + 1
9 ... 165 ............. 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