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Triangle read by rows: T(n,k) is the number of paths traveling orthogonally on an n X k grid that visit every cell.
1

%I #16 Oct 09 2023 14:00:52

%S 1,1,4,1,8,20,1,14,62,276,1,22,132,1006,4324,1,32,336,3610,26996,

%T 229348,1,44,688,12010,109722,1620034,13535280,1,58,1578,38984,602804,

%U 12071462,175905310,3023313284,1,74,3190,122188,2434670,82550864,1449655468,43551685370,745416341496

%N Triangle read by rows: T(n,k) is the number of paths traveling orthogonally on an n X k grid that visit every cell.

%e T(n,k) is a triangular array read by rows:

%e 1,

%e 1, 4,

%e 1, 8, 20,

%e 1, 14, 62, 276,

%e ...

%e T(2,2) = 4:

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

%e | | | | | | | | | | | |

%e | **|** | | * | * | | **|** | | **|** |

%e | | * | | * | * | | * | | | * | * |

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

%e | | * | | * | * | | * | | | * | * |

%e | **|** | | **|** | | **|** | | * | * |

%e | | | | | | | | | | | |

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

%Y See A332307 for another version.

%Y Cf. A120443 (T(n,n)), A366411 (row sums).

%K tabl,nonn,walk

%O 1,3

%A _Douglas Boffey_, Oct 09 2023

%E More terms (using A332307) from _Pontus von Brömssen_, Oct 09 2023