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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 (list; graph; refs; listen; history; text; internal format)
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 * A158515 A285884 A123709

Adjacent sequences:  A242286 A242287 A242288 * A242290 A242291 A242292

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 10 2014

STATUS

approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)