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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
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
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
KEYWORD
nonn,tabl
AUTHOR
Matthew Fahrbach, Apr 15 2019
STATUS
approved