A307584 - OEIS

%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