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%I #52 Jan 12 2023 19:28:11
%S 0,1,2,0,8,9,4,16,5,0,27,28,20,35,18,7,54,28,8,0,64,65,54,72,49,32,91,
%T 56,27,10,128,81,40,11,0,125,126,112,133,104,81,152,108,70,44,189,130,
%U 77,36,13,250,176,108,52,14,0,216,217,200,224,189,160,243
%N a(n) = value of the cubic form A^3 + B^3 + C^3 - 3ABC evaluated at row n of the table in A331195.
%C No term in the sequence is congruent to 3 or 6 (mod 9).
%H Mehmet A. Ates, <a href="/A332616/b332616.txt">Table of n, a(n) for n = 0..19599</a>
%H Mathematical Association of America, <a href="https://www.maa.org/sites/default/files/pdf/Putnam/2019/2019PutnamProblems.pdf">2019 William Lowell Putnam Mathematical Competition Problems</a>
%F a(n) = A056556(n)^3 + A056557(n)^3 + A056558(n)^3 - 3*A056556(n)*A056557(n)*A056558(n).
%e For n=3, a(n) = f[1,1,0] = 1^3 + 1^3 + 0^3 - 3*1*1*0 = 2.
%t SeqSize = 30;
%t ListSize = 120;
%t F3List = List[];
%t f3[a_, b_, c_] := a^3 + b^3 + c^3 - 3*a*b*c
%t For[i = 0, i <= SeqSize, i++, For[j = 0, j <= i, j++, For[k = 0, k <= j, k++, AppendTo[F3List, f3[i, j, k]]]]]
%t ListPlot[F3List, PlotLabel -> "a(n)"]
%t Print["First ", ListSize, " elements of a(n): ", Take[F3List, ListSize]]
%Y Cf. A056556, A056557, A056558.
%Y Cf. A330013, A331195.
%Y Cf. A074232 (in ascending order, strictly positive & without duplicates).
%K nonn,look
%O 0,3
%A _Mehmet A. Ates_, Jun 08 2020
%E Edited by _N. J. A. Sloane_, Aug 06 2020
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