A049761 Triangular array T, read by rows: T(n,k) = n^3 mod k, for k = 1..n and n >= 1.

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 3, 3, 1, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 4, 3, 1, 1, 0, 0, 0, 1, 0, 0, 4, 6, 0, 1, 0, 0, 1, 2, 3, 1, 5, 1, 3, 8, 1, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 8, 1, 0, 0, 1, 1, 1, 2, 1, 6, 5, 1, 7, 8, 1, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  0;
  0, 0;
  0, 1, 0;
  0, 0, 1, 0;
  0, 1, 2, 1, 0;
  0, 0, 0, 0, 1, 0;
  0, 1, 1, 3, 3, 1, 0;
  0, 0, 2, 0, 2, 2, 1, 0;
  0, 1, 0, 1, 4, 3, 1, 1, 0;
  0, 0, 1, 0, 0, 4, 6, 0, 1, 0;
  0, 1, 2, 3, 1, 5, 1, 3, 8, 1, 0;
  ...
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Row sums are in A049762.

Cf. A049759, A049760, A049763, A049764.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> PowerMod(n,3,k) ))); # G. C. Greubel, Dec 13 2019

Magma

[[Modexp(n,3,k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019

Maple

seq(seq( `mod`(n^3, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019

Mathematica

Table[PowerMod[n,3,k], {n,15}, {k, n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)

PARI

T(n,k) = lift(Mod(n,k)^3);
for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 13 2019

Sage

[[power_mod(n,3,k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019