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Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

The Suzuki group is the sporadic group Suz of order |Suz| = 448345497600 (1) = 2^(13)·3^7·5^2·7·11·13. (2) It is implemented in the Wolfram Language as SuzukiGroupSuz[].

By the definition of the trigonometric functions, cos0 = 1 (1) cot0 = infty (2) csc0 = infty (3) sec0 = 1 (4) sin0 = 0 (5) tan0 = 0. (6)

A set of m distinct positive integers S={a_1,...,a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i,j=1, ..., m with i!=j, ...

The Jacobsthal numbers are the numbers obtained by the U_ns in the Lucas sequence with P=1 and Q=-2, corresponding to a=2 and b=-1. They and the Jacobsthal-Lucas numbers (the ...

A prime constellation of four successive primes with minimal distance (p,p+2,p+6,p+8). The term was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The quadruplet (2, ...

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

For |q|<1, the Rogers-Ramanujan identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...