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

1,2

Links

Table of n, a(n) for n=1..68.

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.

Example

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;
...

Crossrefs

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

Sequence in context: A208763 A355721 A249027 * A266183 A232483 A338870

Adjacent sequences: A307581 A307582 A307583 * A307585 A307586 A307587

Keyword

nonn,tabl

Author

Matthew Fahrbach, Apr 15 2019

Status

approved