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

0,13

Comments

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

Links

Table of n, a(n) for n=0..44.

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

Formula

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

Example

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;
  ...

Crossrefs

T(2n,n) gives: A350680.

Sequence in context: A076837 A055363 A363845 * A110855 A054673 A155103

Adjacent sequences: A350678 A350679 A350680 * A350682 A350683 A350684

Keyword

nonn,tabl,more

Author

Colin Defant, Jan 11 2022

Status

approved