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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103999 Square array T(M,N) read by antidiagonals: number of dimer tilings of a 2M x 2N Klein bottle. 5
1, 1, 1, 1, 6, 1, 1, 16, 34, 1, 1, 54, 196, 198, 1, 1, 196, 1666, 2704, 1154, 1, 1, 726, 16384, 64152, 37636, 6726, 1, 1, 2704, 171394, 1844164, 2549186, 524176, 39202, 1, 1, 10086, 1844164, 57523158, 220581904, 101757654, 7300804, 228486, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..45.

Cliff, Danny and Zoe Stoll, About Klein bottles

W. T. Lu and F. Y. Fu, Dimer statistics on the Moebius strip and the Klein bottle, arXiv:cond-mat/9906154 [cond-mat.stat-mech], 1999.

FORMULA

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

EXAMPLE

1,1,1,1,1,1,1,

1,6,34,198,1154,6726,39202,

1,16,196,2704,37636,524176,7300804,

1,54,1666,64152,2549186,101757654,4064620168,

1,196,16384,1844164,220581904,26743369156,3252222705664,

1,726,171394,57523158,21050622914,7902001927776,2988827208115522,

MATHEMATICA

T[m_, n_] := Product[4 Sin[(4k-1) Pi/(4n)]^2 + 4 Cos[j Pi/(2m+1)]^2, {j, 1, m}, {k, 1, n}] // Round;

Table[T[m-n, n], {m, 0, 9}, {n, 0, m}] // Flatten (* Jean-Fran├žois Alcover, Aug 20 2018 *)

CROSSREFS

Rows include A003499, A067902+2. Columns include A003500+2.

Cf. A099390, A103997.

Sequence in context: A176560 A152602 A119726 * A154985 A157275 A157268

Adjacent sequences:  A103996 A103997 A103998 * A104000 A104001 A104002

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Feb 26 2005

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 November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)