A288518 - OEIS

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A288518

Array read by antidiagonals: T(m,n) = number of (undirected) paths in the grid graph P_m X P_n.

0, 1, 1, 3, 12, 3, 6, 49, 49, 6, 10, 146, 322, 146, 10, 15, 373, 1618, 1618, 373, 15, 21, 872, 7119, 14248, 7119, 872, 21, 28, 1929, 28917, 111030, 111030, 28917, 1929, 28, 36, 4118, 111360, 801756, 1530196, 801756, 111360, 4118, 36

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Paths of length zero are not counted here.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..276

Eric Weisstein's World of Mathematics, Graph Path

Eric Weisstein's World of Mathematics, Grid Graph

EXAMPLE

Table starts:

=================================================================

m\n| 1 2 3 4 5 6 7

---|-------------------------------------------------------------

1 | 0 1 3 6 10 15 21 ...

2 | 1 12 49 146 373 872 1929 ...

3 | 3 49 322 1618 7119 28917 111360 ...

4 | 6 146 1618 14248 111030 801756 5493524 ...

5 | 10 373 7119 111030 1530196 19506257 235936139 ...

6 | 15 872 28917 801756 19506257 436619868 9260866349 ...

7 | 21 1929 111360 5493524 235936139 9260866349 343715004510 ...

...

CROSSREFS

Rows 2-7 are A288516, A288527, A358800, A358801, A358802, A358803.

Main diagonal is A288032.

Cf. A231829, A064298, A271465, A271592, A120443, A001184, A145157, A003763.

Sequence in context: A110121 A321710 A358325 * A069522 A170857 A227106

Adjacent sequences: A288515 A288516 A288517 * A288519 A288520 A288521

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Jun 10 2017

STATUS

approved