A242290 - OEIS

%I #4 May 15 2014 10:16:41

%S 5,6,8,9,10,11,14,15,19,20,21,23,24,25,27,29,30,33,34,35,38,40,41,43,

%T 44,45,47,48,49,50,51,54,55,56,59,61,63,64,65,67,68,69,70,71,74,75,76,

%U 78,79,81,83,85,90,93,98,99,104,105,106,107,108,109,110,114

%N Positive integers k for which the k-th tetrahedral number is greedy-summable.

%C Greedy summability is defined at A242288.

%H Clark Kimberling, <a href="/A242290/b242290.txt">Table of n, a(n) for n = 1..1000</a>

%e Let s(n) = n(n+1)(n+2)/6 = A000292(n).  Then

%e a(1) = 5; s(5) = 35 = 20 + 10 + 4 + 1;

%e a(2) = 6; s(6) = 56 = 35 + 20 + 1;

%e a(3) = 8; s(8) = 120 = 84 + 35 + 1;

%e a(4) = 9; s(9) = 165 = 120 + 35 + 10.

%t 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}]

%t r[n_] := s[[n]] - Total[t[[n]][[2]]];

%t tr = Table[r[n], {n, 2, z}]  (* A242288 *)

%t c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242289 *)

%t f = 1 + Flatten[Position[tr, 0]]  (* A242290 *)

%t f (f + 1)(f + 2)/6  (* A242291 *) (* _Peter J. C. Moses_, May 06 2014 *)

%Y Cf. A242288, A242289, A242291, A241833, A242284, A000292.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 10 2014