A049800 Triangular array T, read by rows: T(n,k) = (n+1) mod floor((k+1)/2), k = 1..n and n >= 1.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 1, 1, 2, 2, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 4, 4, 2, 2, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

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

Links

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

Crossrefs

One-half the row sums are in A049798.

Cf. A049799, A049801.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> (n+1) mod Int((k+1)/2) ))); # G. C. Greubel, Dec 09 2019

Magma

[ (n+1) mod Floor((k+1)/2): k in [1..n], n in [1..15]]; // G. C. Greubel, Dec 09 2019

Maple

# To get the sequence:
seq(seq((n+1) mod floor((k+1)/2), k = 1..n), n = 1..30);
# To get the triangular array:
for n from 1 to 30 do
    seq((n+1) mod floor((k+1)/2), k = 1..n);
end do; # Petros Hadjicostas, Nov 20 2019

Mathematica

Table[Mod[n+1, Floor[(k+1)/2]], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Dec 09 2019 *)

PARI

T(n,k) = lift(Mod(n+1,(k+1)\2));
for(n=1, 15, for(k=1, n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 09 2019

Sage

[[ mod(n+1, floor((k+1)/2)) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 09 2019

Extensions

Name edited by Petros Hadjicostas, Nov 20 2019