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A097469
Decimal expansion of growth constant C for dimer model on square grid.
6
1, 3, 3, 8, 5, 1, 5, 1, 5, 1, 9, 7, 6, 0, 9, 6, 7, 6, 6, 9, 3, 8, 1, 9, 5, 9, 0, 2, 0, 1, 8, 5, 1, 3, 5, 3, 7, 0, 6, 4, 3, 5, 3, 6, 9, 7, 1, 2, 7, 9, 1, 1, 3, 1, 4, 6, 4, 1, 2, 3, 4, 7, 8, 6, 6, 2, 2, 3, 9, 1, 1, 3, 3, 0, 0, 7, 9, 8, 0, 9, 7, 8, 6, 4, 6, 4, 8, 7, 3, 8, 4, 6, 1, 7, 7, 4, 4
OFFSET
1,2
LINKS
F. Ardila and R. P. Stanley, Tilings, arXiv:math/0501170 [math.CO], 2005.
P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.
J. Propp, Enumeration of matchings: problems and progress, in New Perspectives in Algebraic Combinatorics
FORMULA
Equals e^(G/Pi), with G = A006752 (Catalan's constant).
Equals exp((1/Pi^2) * Integral_{x=0..Pi/2, y=0..Pi/2} log(4*cos(x)^2 + 4*cos(y)^2) dx dy). - Vaclav Kotesovec, Jan 04 2021
EXAMPLE
1.33851515197609676693819590201851353706435369712791131464123...
MATHEMATICA
RealDigits[Exp[Catalan/Pi], 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)
PROG
(PARI) default(realprecision, 100); exp(Catalan/Pi) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(Catalan(R)/Pi(R)); // G. C. Greubel, Aug 25 2018
CROSSREFS
Cf. A000796 (Pi), A006752 (Catalan's constant).
Sequence in context: A016606 A341616 A069462 * A372409 A279727 A267092
KEYWORD
cons,nonn
AUTHOR
Ralf Stephan, Sep 18 2004
EXTENSIONS
Terms a(14) onward corrected by G. C. Greubel, Aug 26 2018
STATUS
approved