A271465 Array read by antidiagonals: T(n,m) = number of self-avoiding walks of any length from NW to SW corners on a grid with n rows and m columns.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 11, 8, 1, 1, 5, 28, 38, 16, 1, 1, 6, 69, 178, 126, 32, 1, 1, 7, 168, 844, 1008, 415, 64, 1, 1, 8, 407, 4012, 8590, 5493, 1369, 128, 1, 1, 9, 984, 19072, 74148, 81445, 29879, 4521, 256, 1

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..378

Formula

T(1,n)=1, T(2,n)=n, T(n,1)=1, T(n,2)=2^(n-1).

Example

The start of the sequence as table:
*  1   1    1     1        1         1         1 ...
*  1   2    3     4        5         6         7 ...
*  1   4   11    28       69       168       407 ...
*  1   8   38   178      844      4012     19072 ...
*  1  16  126  1008     8590     74148    638472 ...
*  1  32  415  5493    81445   1246850  19011465 ...
*  1  64 1369  29879  761047  20477490 550254085 ...
*  ...

Crossrefs

Main diagonal is A271507. Rows include A005409, A214931. Columns include A006189, A216211. Cf. A064298 (paths from NW to SE).

Sequence in context: A111669 A336573 A124834 * A104495 A093541 A336187

Adjacent sequences: A271462 A271463 A271464 * A271466 A271467 A271468

Keyword

nonn,tabl

Author

Andrew Howroyd, Apr 08 2016

Status

approved