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

Author

Ralf Stephan, Sep 18 2004

Keywords

• cons
• nonn

Examples

			1.33851515197609676693819590201851353706435369712791131464123...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 1.8.3 and 5.23.1, pp. 63, 407.

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

Crossrefs

Cf. A038758, A054344, A130834, A143233.

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

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); Exp(Catalan(R)/Pi(R)); // G. C. Greubel, Aug 25 2018

Mathematica

RealDigits[Exp[Catalan/Pi], 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)

PARI

default(realprecision, 100); exp(Catalan/Pi) \\ G. C. Greubel, Aug 25 2018

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

Equals sqrt(A130834) = exp(A143233). - Hugo Pfoertner, Nov 18 2024

Extensions

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