A307584 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.

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, 22, 1, 2, 46, 330, 838, 722, 222, 26, 1, 2, 54, 490, 1774, 2514, 1382, 314, 30, 1, 2, 62, 682, 3254, 6802, 6062, 2362, 422, 34, 1, 2, 70, 906, 5406, 15378, 20406, 12570, 20406, 12570, 3726, 546, 38, 1

Offset: 1

Author

Matthew Fahrbach, Apr 15 2019

Keywords

• nonn
• tabl

Examples

			Triangle begins:
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,    22,     1;
2, 46, 330,  838,   722,   222,    26,    1;
2, 54, 490, 1774,  2514,  1382,   314,   30,   1;
2, 62, 682, 3254,  6802,  6062,  2362,  422,  34,  1;
2, 70, 906, 5406, 15378, 20406, 12570, 3726, 546, 38, 1;
...
		

Links

• M. Fahrbach and D. Randall, Slow mixing of Glauber dynamics for the six-vertex model in the ferroelectric and antiferroelectric phases, arXiv:1904.01495 [cs.DS], 2019
• R. J. Mathar, Walks of up and right steps in the square lattice with blocked squares (2022) Table 2.

Crossrefs

Row sums give A000244. Cf. A051708 (subdiagonal T(2n,n)).