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A103997 Square array T(M,N) read by antidiagonals: number of dimer tilings of a 2*M X 2*N 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 (list; table; graph; refs; listen; history; text; internal format)
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, arXiv:cond-mat/9906154 [cond-mat.stat-mech], 1999.

FORMULA

T(M, N) = Product_{m=1..M} (Product_{n=1..N} 4*sin(Pi*(4*n-1)/(4*N))^2 + 4*cos(Pi*m/(2*M + 1))^2).

EXAMPLE

Array begins:

  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,

  ...

MATHEMATICA

T[M_, N_] := Product[4Sin[(4n-1)Pi/(4N)]^2 + 4Cos[m Pi/(2M+1)]^2, {n, 1, N}, {m, 1, M}];

Table[T[M - N, N] // Round, {M, 0, 9}, {N, 0, M}] // Flatten (* Jean-Fran├žois Alcover, Dec 03 2018 *)

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

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)