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A212796
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Square array read by antidiagonals: T(m,n) = number of spanning trees in C_m X C_n.
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4
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1, 2, 2, 3, 32, 3, 4, 294, 294, 4, 5, 2304, 11664, 2304, 5, 6, 16810, 367500, 367500, 16810, 6, 7, 117600, 10609215, 42467328, 10609215, 117600, 7, 8, 799694, 292626432, 4381392020, 4381392020, 292626432, 799694, 8, 9, 5326848, 7839321861, 428652000000, 1562500000000, 428652000000, 7839321861, 5326848, 9
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OFFSET
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1,2
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REFERENCES
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G. Kreweras, Complexite et circuits Euleriens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Parag. 4.
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LINKS
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Table of n, a(n) for n=1..45.
Eric Weisstein's World of Mathematics, Spanning Tree
Eric Weisstein's World of Mathematics, Torus Grid Graph
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FORMULA
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T(m,n) = m*n*Prod(Prod( 4*sin(h*Pi/m)^2+4*sin(k*Pi/n)^2, h=1..m-1), k=1..n-1).
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EXAMPLE
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Array begins:
1, 2, 3, 4, 5, 6, ...
2, 32, 294, 2304, 16810, 117600, 799694, 5326848, 34928082, 226195360, ...
3, 294, 11664, 367500, 10609215, 292626432, 7839321861, 205683135000, ...
4, 2304, 367500, 42467328, 4381392020, 428652000000, 40643137651228, ...
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MAPLE
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Digits:=200;
T:=(m, n)->round(Re(evalf(simplify(expand(
m*n*mul(mul( 4*sin(h*Pi/m)^2+4*sin(k*Pi/n)^2, h=1..m-1), k=1..n-1))))));
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CROSSREFS
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Diagonals give A212797, A212798, A212799, A212800.
Cf. A116469, A173958.
Sequence in context: A109590 A074935 A320103 * A078239 A083113 A184847
Adjacent sequences: A212793 A212794 A212795 * A212797 A212798 A212799
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, May 27 2012
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STATUS
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approved
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