login
Triangle read by rows: T(m,n) is the number of simple paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an m X n grid, 1 <= n <= m.
3

%I #15 Feb 18 2023 08:06:12

%S 1,1,3,1,6,23,2,17,118,1470,3,47,762,23878,914525,5,133,5724,420894,

%T 40285572

%N Triangle read by rows: T(m,n) is the number of simple paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an m X n grid, 1 <= n <= m.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Racetrack_(game)">Racetrack</a>

%e Triangle begins:

%e m\n| 1 2 3 4 5 6

%e ---+------------------------------

%e 1 | 1

%e 2 | 1 3

%e 3 | 1 6 23

%e 4 | 2 17 118 1470

%e 5 | 3 47 762 23878 914525

%e 6 | 5 133 5724 420894 40285572 ?

%Y Cf. A291896 (column n=1), A329118, A351041, A351107 (main diagonal), A351108, A351110.

%K nonn,tabl,more

%O 1,3

%A _Pontus von Brömssen_, Jan 31 2022