A329118 Array read by antidiagonals: T(m, n) is the number of simple paths from corner to diagonally opposite corner on an m X n grid with king moves allowed.

1, 1, 1, 1, 5, 1, 1, 24, 24, 1, 1, 116, 235, 116, 1, 1, 560, 2922, 2922, 560, 1, 1, 2704, 38169, 96371, 38169, 2704, 1, 1, 13056, 494596, 3764367, 3764367, 494596, 13056, 1, 1, 63040, 6375379, 150610151, 447544629, 150610151, 6375379, 63040, 1, 1, 304384, 82191766, 5898799685, 56182569218, 56182569218, 5898799685, 82191766, 304384, 1

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..231

Example

Array begins:
===================================================================
m\n | 1     2       3          4             5                6
----+--------------------------------------------------------------
  1 | 1     1       1          1             1                1 ...
  2 | 1     5      24        116           560             2704 ...
  3 | 1    24     235       2922         38169           494596 ...
  4 | 1   116    2922      96371       3764367        150610151 ...
  5 | 1   560   38169    3764367     447544629      56182569218 ...
  6 | 1  2704  494596  150610151   56182569218   22132498074021 ...
  7 | 1 13056 6375379 5898799685 6972159602221 8656506756327178 ...
  ...

Crossrefs

Rows 2..6 are A086347, A193168, A193170, A193171, A193172.

Main diagonal is A140518.

Cf. A158651, A272445, A288033.

Sequence in context: A359993 A157212 A156600 * A152572 A203346 A176793

Adjacent sequences: A329115 A329116 A329117 * A329119 A329120 A329121

Keyword

nonn,walk,tabl

Author

Andrew Howroyd, Nov 05 2019

Status

approved