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A276994 Decimal expansion of the Klarner-Rivest polyomino constant. 3
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Analytic Combinatorics (Flajolet and Sedgewick, 2009, p. 662) has a wrong value of this constant (2.309138593331230...).

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.19 (Klarner's polyomino constant), p. 380.

LINKS

Table of n, a(n) for n=1..105.

E. A. Bender, Convex n-ominoes, Discrete Math., 8 (1974), 219-226.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009, p. 662.

D. A. Klarner and R. L. Rivest, Asymptotic bounds for the number of convex n-ominoes, Discrete Math., 8 (1974), 31-40.

FORMULA

Equals lim n -> infinity A006958(n)^(1/n).

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.

EXAMPLE

2.309138593330494731098720305017212531911814472581628401694402900284456440748...

MATHEMATICA

1/z/.FindRoot[Sum[(-1)^n * z^(n*(n+1)/2) / QPochhammer[z, z, n]^2, {n, 0, 1000}], {z, 2/5}, WorkingPrecision -> 120]

CROSSREFS

Cf. A006958.

Sequence in context: A120473 A019911 A173344 * A020823 A021437 A074760

Adjacent sequences:  A276991 A276992 A276993 * A276995 A276996 A276997

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Sep 27 2016

STATUS

approved

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)