A224273 Decimal expansion of Baxter's four-coloring constant.

1, 4, 6, 0, 9, 9, 8, 4, 8, 6, 2, 0, 6, 3, 1, 8, 3, 5, 8, 1, 5, 8, 8, 7, 3, 1, 1, 7, 8, 4, 6, 0, 5, 9, 6, 9, 7, 0, 3, 8, 9, 3, 1, 3, 5, 5, 8, 0, 7, 4, 6, 1, 7, 8, 8, 2, 0, 5, 7, 7, 5, 4, 3, 4, 4, 4, 1, 5, 2, 1, 3, 5, 5, 8, 8, 5, 7, 3, 1, 4, 4, 0, 7, 7, 6, 5, 3

Offset: 1

Author

Bruno Berselli, Apr 02 2013

Keywords

• nonn
• cons

Comments

The constant is named after Australian physicist Rodney James Baxter. - Amiram Eldar, Aug 13 2020

Examples

			1.46099848620631835815887311784605969703893135580746178820577543...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See p. 413.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• R. J. Baxter, Colorings of a hexagonal lattice, Journal of Mathematical Physics, Vol. 11, No. 3 (1970), pp. 784-789.
• R. J. Baxter, q colourings of the triangular lattice, Journal of Physics A: Mathematical and General, Vol. 19, No. 14 (1986), pp. 2821-2839.
• Eric Weisstein's World of Mathematics, Baxter's Four-Coloring Constant.

Crossrefs

Cf. A004117, A081760, A152751.

Programs

Mathematica

RealDigits[3 Gamma[1/3]^3/(4 Pi^2), 10, 90][[1]]

PARI

3*gamma(1/3)^3/(4*Pi^2) \\ Michel Marcus, Mar 23 2020

Formula

Equals 1/Product_{n>=1} (1-1/(3n-1)^2) = 3*Gamma(1/3)^3/(4*Pi^2).

Equals 1/(2^(1/3)*A081760). - Kritsada Moomuang, Mar 15 2020

Equals 2*Pi/(sqrt(3)*Gamma(2/3)^3). - Vaclav Kotesovec, Mar 23 2020

Equals Product_{k>=1} (1 + 1/A152751(k)). - Amiram Eldar, Aug 13 2020

Equals Sum_{k>=0} binomial(-1/3, k)^2. - Gerry Martens, Jul 24 2023