The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 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 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-François 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.

Last modified August 4 06:58 EDT 2020. Contains 336201 sequences. (Running on oeis4.)