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 A212796 Square array read by antidiagonals: T(m,n) = number of spanning trees in C_m X C_n. 4
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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. LINKS Eric Weisstein's World of Mathematics, Spanning Tree Eric Weisstein's World of Mathematics, Torus Grid Graph FORMULA 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). EXAMPLE 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, ... ... MAPLE 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)))))); CROSSREFS 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 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, May 27 2012 STATUS approved

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Last modified December 9 23:02 EST 2019. Contains 329880 sequences. (Running on oeis4.)