login
Array read by antidiagonals: T(n,m) is the number of matchings in the torus grid graph C_n X C_m.
3

%I #17 Aug 04 2024 15:13:34

%S 1,2,2,4,7,4,7,32,32,7,11,108,370,108,11,18,342,2764,2764,342,18,29,

%T 1104,19874,41025,19874,1104,29,47,3544,144108,576287,576287,144108,

%U 3544,47,76,11396,1043060,8205424,15637256,8205424,1043060,11396,76

%N Array read by antidiagonals: T(n,m) is the number of matchings in the torus grid graph C_n X C_m.

%H Andrew Howroyd, <a href="/A270246/b270246.txt">Table of n, a(n) for n = 1..284</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>

%F T(1, m) = A000032(m) for m<>2.

%e The start of the sequence as table:

%e * 1 2 4 7 11 18 ...

%e * 2 7 32 108 342 1104 ...

%e * 4 32 370 2764 19874 144108 ...

%e * 7 108 2764 41025 576287 8205424 ...

%e * 11 342 19874 576287 15637256 430996378 ...

%e * 18 1104 144108 8205424 430996378 23079663560 ...

%e * ...

%Y Main diagonal is A270247. Row 2 is A102080.

%K nonn,tabl

%O 1,2

%A _Andrew Howroyd_, Mar 13 2016