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%I #36 Sep 27 2016 16:00:37
%S 2,3,0,9,1,3,8,5,9,3,3,3,0,4,9,4,7,3,1,0,9,8,7,2,0,3,0,5,0,1,7,2,1,2,
%T 5,3,1,9,1,1,8,1,4,4,7,2,5,8,1,6,2,8,4,0,1,6,9,4,4,0,2,9,0,0,2,8,4,4,
%U 5,6,4,4,0,7,4,8,3,1,6,8,4,2,7,1,7,2,8,1,6,1,5,7,7,4,4,1,2,1,7,4,3,7,4,6,1
%N Decimal expansion of the Klarner-Rivest polyomino constant.
%C Analytic Combinatorics (Flajolet and Sedgewick, 2009, p. 662) has a wrong value of this constant (2.309138593331230...).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.19 (Klarner's polyomino constant), p. 380.
%H E. A. Bender, <a href="http://dx.doi.org/10.1016/0012-365X(74)90134-4">Convex n-ominoes</a>, Discrete Math., 8 (1974), 219-226.
%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009, p. 662.
%H D. A. Klarner and R. L. Rivest, <a href="http://people.csail.mit.edu/rivest/pubs/KR74.pdf">Asymptotic bounds for the number of convex n-ominoes</a>, Discrete Math., 8 (1974), 31-40.
%F Equals lim n -> infinity A006958(n)^(1/n).
%F 1/A276994 = 0.4330619231293906645846169654189837... is the smallest positive root of the equation Sum_{n>=0} ((-1)^n * z^(n*(n+1)/2) / (Product_{k=1..n} 1-z^k)^2) = 0.
%e 2.309138593330494731098720305017212531911814472581628401694402900284456440748...
%t 1/z/.FindRoot[Sum[(-1)^n * z^(n*(n+1)/2) / QPochhammer[z, z, n]^2, {n, 0, 1000}], {z, 2/5}, WorkingPrecision -> 120]
%Y Cf. A006958.
%K nonn,cons
%O 1,1
%A _Vaclav Kotesovec_, Sep 27 2016