A350681 Triangle read by rows. T(n,k) is the number of hitomezashi loops of width 2(n-k)+1 and height 2k+1 for 0 <= k <= n.

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 8, 11, 8, 1, 0, 0, 1, 16, 27, 27, 16, 1, 0, 0, 1, 32, 64, 76, 64, 32, 1, 0

Offset: 0

Author

Colin Defant, Jan 11 2022

Keywords

• nonn
• tabl
• more

Comments

The Defant--Kravitz paper proves that every hitomezashi loop has odd width and odd height.

Examples

			Triangle T(n,k) begins:
  1;
  0, 0;
  0, 1,  0;
  0, 1,  1,  0;
  0, 1,  2,  1,  0;
  0, 1,  4,  4,  1,  0;
  0, 1,  8, 11,  8,  1,  0;
  0, 1, 16, 27, 27, 16,  1, 0;
  0, 1, 32, 64, 76, 64, 32, 1, 0;
  ...
		

Links

• Colin Defant and Noah Kravitz, Loops and Regions in Hitomezashi Patterns, arXiv:2201.03461 [math.CO], 2022.

Crossrefs

T(2n,n) gives: A350680.

Formula

T(n,k) = T(n,n-k).