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Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

A polybe is a polyform formed from a polycubes by removing of half of each cube such that at least half of the original join between cubes is retained. The numbers of polybes ...

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, ...

A prime p_n is called "good" if p_n^2>p_(n-i)p_(n+i) for all 1<=i<=n-1 (there is a typo in Guy 1994 in which the is are replaced by 1s). There are infinitely many good ...

The thinnest sequence which contains 1, and whenever it contains x, also contains 2x, 3x+2, and 6x+3: 1, 2, 4, 5, 8, 9, 10, 14, 15, 16, 17, ... (OEIS A005658).

The cyclic group C_8 is one of the three Abelian groups of the five groups total of group order 8. Examples include the integers modulo 8 under addition (Z_8) and the residue ...

A number given by the generating function (2t)/(e^t+1)=sum_(n=1)^inftyG_n(t^n)/(n!). (1) It satisfies G_1=1, G_3=G_5=G_7=...=0, and even coefficients are given by G_(2n) = ...

A number which is simultaneously a nonagonal number N_m and hexagonal number Hex_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=n(2n-1). (1) Completing the ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...

The snub cube, also called the cubus simus (Kepler 1619, Weissbach and Martini 2002) or snub cuboctahedron, is an Archimedean solid having 38 faces (32 triangular and 6 ...