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%I #24 Jan 26 2022 09:41:30
%S 1,2,1,2,6,1,2,14,10,1,2,22,42,14,1,2,30,106,86,18,1,2,38,202,318,146,
%T 22,1,2,46,330,838,722,222,26,1,2,54,490,1774,2514,1382,314,30,1,2,62,
%U 682,3254,6802,6062,2362,422,34,1,2,70,906,5406,15378,20406,12570,20406,12570,3726,546,38,1
%N Triangle read by rows: T(n,k) is the number of non-backtracking walks on Z^2 of length n that are active for k steps, where the walk is initially active and turns in the walk toggle the activity.
%H M. Fahrbach and D. Randall, <a href="https://arxiv.org/abs/1904.01495">Slow mixing of Glauber dynamics for the six-vertex model in the ferroelectric and antiferroelectric phases</a>, arXiv:1904.01495 [cs.DS], 2019
%H R. J. Mathar, <a href="/A348595/a348595.pdf">Walks of up and right steps in the square lattice with blocked squares</a> (2022) Table 2.
%e Triangle begins:
%e 1;
%e 2, 1;
%e 2, 6, 1;
%e 2, 14, 10, 1;
%e 2, 22, 42, 14, 1;
%e 2, 30, 106, 86, 18, 1;
%e 2, 38, 202, 318, 146, 22, 1;
%e 2, 46, 330, 838, 722, 222, 26, 1;
%e 2, 54, 490, 1774, 2514, 1382, 314, 30, 1;
%e 2, 62, 682, 3254, 6802, 6062, 2362, 422, 34, 1;
%e 2, 70, 906, 5406, 15378, 20406, 12570, 3726, 546, 38, 1;
%e ...
%Y Row sums give A000244. Cf. A051708 (subdiagonal T(2n,n)).
%K nonn,tabl
%O 1,2
%A _Matthew Fahrbach_, Apr 15 2019