A049801 Triangular array T, read by rows: T(n,k) = n mod floor(k/3), k = 3..n and n >= 3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 3, 3, 3, 0

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Array T(n,k) (with rows n >= 3 and columns k >= 3) begins as follows:
  0;
  0, 0;
  0, 0, 0;
  0, 0, 0, 0;
  0, 0, 0, 1, 1;
  0, 0, 0, 0, 0, 0;
  0, 0, 0, 1, 1, 1, 0;
  0, 0, 0, 0, 0, 0, 1, 1;
  0, 0, 0, 1, 1, 1, 2, 2, 2;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
  0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1;
  0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2;
  ...
		

Links

• G. C. Greubel, Rows n = 3..100 of triangle, flattened

Crossrefs

Row sums are in A049799.

Cf. A049797, A049798, A049800.

Programs

GAP

Flat(List([3..15], n-> List([3..n], k-> n mod Int(k/3) ))); # G. C. Greubel, Dec 09 2019

Magma

[ n mod Floor(k/3): k in [3..n], n in [3..15]]; // G. C. Greubel, Dec 09 2019

Maple

# To get the sequence:
seq(seq(n mod floor(k/3), k = 3..n), n = 3..30);
# To get the triangular array:
for n from 3 to 30 do
    seq(n mod floor(k/3), k = 3..n);
end do; # Petros Hadjicostas, Nov 20 2019

Mathematica

Table[Mod[n, Floor[k/3]], {n,3,15}, {k,3,n}]//Flatten (* G. C. Greubel, Dec 09 2019 *)

PARI

T(n,k) = lift(Mod(n, k\3)); \\ G. C. Greubel, Dec 09 2019

Sage

[[ mod(n, floor(k/3)) for k in (3..n)] for n in (3..15)] # G. C. Greubel, Dec 09 2019

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 20 2019