%I #15 Jan 12 2022 21:36:50
%S 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,
%T 27,16,1,0,0,1,32,64,76,64,32,1,0
%N 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.
%C The Defant--Kravitz paper proves that every hitomezashi loop has odd width and odd height.
%H Colin Defant and Noah Kravitz, <a href="https://arxiv.org/abs/2201.03461">Loops and Regions in Hitomezashi Patterns</a>, arXiv:2201.03461 [math.CO], 2022.
%F T(n,k) = T(n,n-k).
%e Triangle T(n,k) begins:
%e 1;
%e 0, 0;
%e 0, 1, 0;
%e 0, 1, 1, 0;
%e 0, 1, 2, 1, 0;
%e 0, 1, 4, 4, 1, 0;
%e 0, 1, 8, 11, 8, 1, 0;
%e 0, 1, 16, 27, 27, 16, 1, 0;
%e 0, 1, 32, 64, 76, 64, 32, 1, 0;
%e ...
%Y T(2n,n) gives: A350680.
%K nonn,tabl,more
%O 0,13
%A _Colin Defant_, Jan 11 2022