login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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