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 A224273 Decimal expansion of Baxter's four-coloring constant. 3
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The constant is named after Australian physicist Rodney James Baxter. - Amiram Eldar, Aug 13 2020 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. 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 EXAMPLE 1.46099848620631835815887311784605969703893135580746178820577543... MATHEMATICA RealDigits[3 Gamma[1/3]^3/(4 Pi^2), 10, 90][[1]] PROG (PARI) 3*gamma(1/3)^3/(4*Pi^2) \\ Michel Marcus, Mar 23 2020 CROSSREFS Cf. A004117, A081760, A152751. Sequence in context: A200349 A021221 A197006 * A285444 A285584 A316386 Adjacent sequences: A224270 A224271 A224272 * A224274 A224275 A224276 KEYWORD nonn,cons AUTHOR Bruno Berselli, Apr 02 2013 STATUS approved

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Last modified September 10 12:41 EDT 2024. Contains 375789 sequences. (Running on oeis4.)