A225800 Triangle of rising diagonals of A011973 (with rows displayed as centered text).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 5, 4, 1, 1, 7, 6, 1, 1, 1, 9, 8, 6, 3, 1, 1, 11, 10, 15, 10, 1, 1, 13, 12, 28, 21, 1, 1, 1, 15, 14, 45, 36, 10, 4, 1, 1, 17, 16, 66, 55, 35, 20, 1, 1, 19, 18, 91, 78, 84, 56, 1, 1, 1, 21, 20, 120, 105, 165, 120, 15, 5, 1

Offset: 1

Author

John Molokach, Jul 27 2013

Keywords

• nonn
• tabf

Comments

Row sums are A227300.

Examples

			Triangle begins:
  1;
  1,  1;
  1,  1;
  1,  1,  1;
  1,  1,  3,  2;
  1,  1,  5,  4;
  1,  1,  7,  6,  1;
  1,  1,  9,  8,  6,  3;
  1,  1, 11, 10, 15, 10;
  1,  1, 13, 12, 28, 21,  1;
		

Crossrefs

Cf. A011973, A000045, A227300, A005314, A224838.

Programs

Mathematica

Table[Binomial[2 n - k - 2 - 3 Floor[k/2], Floor[k/2]], {n, 1, 25}, {k, 0, Floor[(2 n - 1)/3]}] (* John Molokach, Jul 29 2013 *)

Formula

r(n) = binomial(2n-k-2-3*floor(k/2), floor(k/2)), k = 0..floor((2n-1)/3). - John Molokach, Jul 29 2013