A332616 a(n) = value of the cubic form A^3 + B^3 + C^3 - 3ABC evaluated at row n of the table in A331195.

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, 56, 27, 10, 128, 81, 40, 11, 0, 125, 126, 112, 133, 104, 81, 152, 108, 70, 44, 189, 130, 77, 36, 13, 250, 176, 108, 52, 14, 0, 216, 217, 200, 224, 189, 160, 243

Offset: 0

Author

Mehmet A. Ates, Jun 08 2020

Keywords

• nonn
• look

Comments

No term in the sequence is congruent to 3 or 6 (mod 9).

Examples

			For n=3, a(n) = f[1,1,0] = 1^3 + 1^3 + 0^3 - 3*1*1*0 = 2.
		

Links

• Mehmet A. Ates, Table of n, a(n) for n = 0..19599
• Mathematical Association of America, 2019 William Lowell Putnam Mathematical Competition Problems

Crossrefs

Cf. A056556, A056557, A056558.

Cf. A330013, A331195.

Cf. A074232 (in ascending order, strictly positive & without duplicates).

Programs

Mathematica

SeqSize = 30;
ListSize = 120;
F3List = List[];
f3[a_, b_, c_] := a^3 + b^3 + c^3 - 3*a*b*c
For[i = 0, i <= SeqSize, i++, For[j = 0, j <= i, j++, For[k = 0, k <= j, k++, AppendTo[F3List, f3[i, j, k]]]]]
ListPlot[F3List, PlotLabel -> "a(n)"]
Print["First ", ListSize, " elements of a(n): ", Take[F3List, ListSize]]

Formula

a(n) = A056556(n)^3 + A056557(n)^3 + A056558(n)^3 - 3*A056556(n)*A056557(n)*A056558(n).

Extensions

Edited by N. J. A. Sloane, Aug 06 2020