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

0,3

Comments

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

Links

Mehmet A. Ates, Table of n, a(n) for n = 0..19599

Mathematical Association of America, 2019 William Lowell Putnam Mathematical Competition Problems

Formula

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

Example

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

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]]

Crossrefs

Cf. A056556, A056557, A056558.

Cf. A330013, A331195.

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

Sequence in context: A287542 A288197 A181592 * A097348 A271034 A185965

Adjacent sequences: A332613 A332614 A332615 * A332617 A332618 A332619

Keyword

nonn,look

Author

Mehmet A. Ates, Jun 08 2020

Extensions

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

Status

approved