A242291 Greedy-summable tetrahedral numbers.

35, 56, 120, 165, 220, 286, 560, 680, 1330, 1540, 1771, 2300, 2600, 2925, 3654, 4495, 4960, 6545, 7140, 7770, 9880, 11480, 12341, 14190, 15180, 16215, 18424, 19600, 20825, 22100, 23426, 27720, 29260, 30856, 35990, 39711, 43680, 45760, 47905, 52394, 54740

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

Cf. A242288, A242289, A242290, A241833, A242284, A000292.

Sequence in context: A090877 A048033 A254366 * A078819 A189554 A351095

Adjacent sequences: A242288 A242289 A242290 * A242292 A242293 A242294

Keyword

nonn,easy

Author

Clark Kimberling, May 10 2014

Status

approved