

A103997


Square array T(M,N) read by antidiagonals: number of dimer tilings of a 2M x 2N Moebius strip.


5



1, 1, 1, 1, 3, 1, 1, 11, 7, 1, 1, 41, 71, 18, 1, 1, 153, 769, 539, 47, 1, 1, 571, 8449, 17753, 4271, 123, 1, 1, 2131, 93127, 603126, 434657, 34276, 322, 1, 1, 7953, 1027207, 20721019, 46069729, 10894561, 276119, 843, 1, 1, 29681, 11332097
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..47.
W. T. Lu and F. Y. Fu, Dimer statistics on the Moebius strip and the Klein bottle


FORMULA

T(M, N) = Prod[m=1..M, Prod[n=1..N, 4sin(Pi*(4n1)/(4N))^2 + 4cos(Pi*m/(2M+1))^2 ]].


EXAMPLE

1,1,1,1,1,1,1,
1,3,7,18,47,123,322,
1,11,71,539,4271,34276,276119,
1,41,769,17753,434657,10894561,275770321,
1,153,8449,603126,46069729,3625549353,289625349454,
1,571,93127,20721019,4974089647,1234496016491,312007855309063,


CROSSREFS

Rows include A005248, A103998. Columns include A001835.
Cf. A099390, A103999.
Sequence in context: A243752 A113711 A257894 * A256895 A223256 A013561
Adjacent sequences: A103994 A103995 A103996 * A103998 A103999 A104000


KEYWORD

nonn,tabl


AUTHOR

Ralf Stephan, Feb 26 2005


STATUS

approved



