A242289 Number of terms in the greedy sum for the n-th tetrahedral number.

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

Clark Kimberling, Table of n, a(n) for n = 2..2000

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

Cf. A242288, A242290, A242291, A241833, A242284, A000292.

Sequence in context: A259582 A139048 A182101 * A349229 A158515 A285884

Adjacent sequences: A242286 A242287 A242288 * A242290 A242291 A242292

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved