A355859 Triangle read by rows: T(n,k) = (n + k)/2 if (n + k) is congruent to 0 (mod 2), otherwise T(n,k) = 0; n >= 1, k >= 1.

1, 0, 2, 2, 0, 3, 0, 3, 0, 4, 3, 0, 4, 0, 5, 0, 4, 0, 5, 0, 6, 4, 0, 5, 0, 6, 0, 7, 0, 5, 0, 6, 0, 7, 0, 8, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 0, 13, 0

Offset: 1

Author

Ctibor O. Zizka, Jul 19 2022

Keywords

• nonn
• tabl

Comments

Row sums see A001318.

Examples

			The triangle begins:
      k=1  2  3  4  5  6
  n=1:  1;
  n=2:  0, 2;
  n=3:  2, 0, 3;
  n=4:  0, 3, 0, 4;
  n=5:  3, 0, 4, 0, 5;
  n=6:  0, 4, 0, 5, 0, 6;
  and so on.
		

Crossrefs

Cf. A001318, A138099 (without the zeros).

Programs

Mathematica

T[n_, k_] := If[EvenQ[n + k], (n + k)/2, 0]; Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 19 2022 *)