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A102856 Sum of 1 or 2 distinct tetrahedral numbers.

%I A102856 #31 Jun 05 2025 10:49:24
%S A102856 0,1,4,5,10,11,14,20,21,24,30,35,36,39,45,55,56,57,60,66,76,84,85,88,
%T A102856 91,94,104,119,120,121,124,130,140,155,165,166,169,175,176,185,200,
%U A102856 204,220,221,224,230,240,249,255,276,285,286,287,290,296,304,306
%N A102856 Sum of 1 or 2 distinct tetrahedral numbers.
%H A102856 Robert Israel, <a href="/A102856/b102856.txt">Table of n, a(n) for n = 1..10000</a>
%p A102856 N:= 1000: # for terms <= N
%p A102856 R:= 0:
%p A102856 for i from 1 do
%p A102856   ti:= i*(i+1)*(i+2)/6;
%p A102856   if ti > N then break fi;
%p A102856   for j from 0 to i-1 do
%p A102856      v:= ti + j*(j+1)*(j+2)/6;
%p A102856      if v > N then break fi;
%p A102856      R:= R, v;
%p A102856   od;
%p A102856 od:
%p A102856 sort(convert({R},list)); # _Robert Israel_, Jan 16 2024
%t A102856 Module[{nn=12, tetra}, tetra=Table[(n(n+1)(n+2))/6, {n, nn}]; Union[ Total/@ Subsets[tetra, 2]]] (* _James C. McMahon_, Jan 12 2024 *)
%Y A102856 Cf. A000292 (subsequence), A010329, A104246, A102795-A102800, A102802-A102806, A102855, A102857, A102858, A334013.
%Y A102856 Cf. A102801 (sums if 2 distinct positive)
%K A102856 nonn
%O A102856 1,3
%A A102856 _Jud McCranie_, Mar 01 2005
%E A102856 a(1) = 0 prepended by _James C. McMahon_, Jan 15 2024