A134513 Triangle read by rows: T(n, k) = binomial(ceiling((n+k)/2), floor((n-k)/2)).

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 3, 1, 1, 3, 3, 4, 4, 1, 1, 1, 6, 6, 5, 5, 1, 1, 4, 4, 10, 10, 6, 6, 1, 1, 1, 10, 10, 15, 15, 7, 7, 1, 1, 5, 5, 20, 20, 21, 21, 8, 8, 1, 1, 1, 15, 15, 35, 35, 28, 28, 9, 9, 1, 1, 6, 6, 35, 35, 56, 56, 36, 36, 10, 10, 1, 1

Offset: 0

Author

Gary W. Adamson, Oct 28 2007

Keywords

• nonn
• tabl

Comments

Old name: abs(A049310 * A097806).

Equivalently, T(n,k) = A168561(n,k) + A168561(n,k+1).

Row sums = A062114: (1, 2, 3, 6, 9, 16, 25, 42, 67, ...).

Triangle A046854 = abs(A097806 * A049310).

Examples

			First few rows of the triangle:
  1;
  1,  1;
  1,  1,  1;
  2,  2,  1,  1;
  1,  3,  3,  1,  1;
  3,  3,  4,  4,  1,  1;
  1,  6,  6,  5,  5,  1,  1;
  4,  4, 10, 10,  6,  6,  1,  1;
  1, 10, 10, 15, 15,  7,  7,  1,  1;
  ...
		

Crossrefs

Cf. A046854, A049310, A062114, A097806.

Formula

abs(A049310 * A097806) as infinite lower triangular matrices.

Extensions

Better definition, offset changed to 0, and more terms from Jinyuan Wang, Jan 25 2025