A097469 Decimal expansion of growth constant C for dimer model on square grid.

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

G. C. Greubel, Table of n, a(n) for n = 1..10000

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. A038758, A054344, A130834.

Cf. A000796 (Pi), A006752 (Catalan's constant).

Sequence in context: A016606 A341616 A069462 * A279727 A267092 A272212

Adjacent sequences: A097466 A097467 A097468 * A097470 A097471 A097472

Keyword

cons,nonn

Author

Ralf Stephan, Sep 18 2004

Extensions

Terms a(14) onward corrected by G. C. Greubel, Aug 26 2018

Status

approved