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A360922
Array read by antidiagonals: T(m,n) is the number of acyclic orientations in the grid graph P_m X P_n.
1
1, 2, 2, 4, 14, 4, 8, 98, 98, 8, 16, 686, 2398, 686, 16, 32, 4802, 58670, 58670, 4802, 32, 64, 33614, 1435414, 5015972, 1435414, 33614, 64, 128, 235298, 35118638, 428816558, 428816558, 35118638, 235298, 128, 256, 1647086, 859207558, 36659327366, 128091434266, 36659327366, 859207558, 1647086, 256
OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..253 (first 22 antidiagonals).
Eric Weisstein's World of Mathematics, Grid Graph.
FORMULA
T(m,n) = T(n,m).
EXAMPLE
Array begins:
=====================================================
m\n| 1 2 3 4 5 ...
---+-------------------------------------------------
1 | 1 2 4 8 16 ...
2 | 2 14 98 686 4802 ...
3 | 4 98 2398 58670 1435414 ...
4 | 8 686 58670 5015972 428816558 ...
5 | 16 4802 1435414 428816558 128091434266 ...
6 | 32 33614 35118638 36659327366 38261306901842 ...
...
CROSSREFS
Main diagonal is A080690.
Rows 1..2 are A000079(n-1), A109808.
Cf. A116469 (spanning trees), A178435, A207868 (unlabeled colorings).
Sequence in context: A248238 A268009 A263224 * A267957 A204978 A204705
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 07 2023
STATUS
approved