A350680 -id:A350680 - cp's OEIS frontend

Showing 1-1 of 1 results.

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.

Original entry on oeis.org

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

Colin Defant, Jan 11 2022

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

			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;
  ...

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

T(2n,n) gives: A350680.

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

Showing 1-1 of 1 results.