A350681 - OEIS

%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