Sequences

a(n) = norm of Heilbronn sum NH_{p}, with p = prime(n).

Coefficients of period polynomials.

Discriminants of period polynomials.

Numbers k such that k^16 + 1 is prime.

Numbers k such that k^8 + 1 is prime.

Numbers n such that n^32 + 1 is prime.

Numbers k such that k^64 + 1 is prime.

Maximum number of chess queens of 3 colors on an n X n board such that no queen attacks or protects another queen of its color.

Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).

Royal paths in a lattice (convolution of A006318).

Royal paths in a lattice.

Royal paths in a lattice.

4-dimensional analog of centered polygonal numbers.

4-dimensional analog of centered polygonal numbers.

a(n) = n*(n + 1)*(2*n^2 + 2*n - 1)/6.

4-dimensional analog of centered polygonal numbers.

Total preorders.

a(n) = Fibonacci(n) - 3. Number of total preorders.

Total preorders.

Total preorders.

Number of corners, or planar partitions of n with only one row and one column.

a(n) = n*(n+1)*(2*n+1)/3.

From the enumeration of corners.

From the enumeration of corners.

From the enumeration of corners.

a(n) = 4^n*(3*n)!/((n+1)!*(2*n+1)!).

a(n) = a(n-1) + a(n - 1 - number of even terms so far).

An "eta-sequence": a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).

An "eta-sequence": floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2).

Least hypotenuse of n distinct Pythagorean triangles.

An "eta-sequence": [ (n+1)*tau + 1/2 ] - [ n*tau + 1/2 ], tau = (1 + sqrt(5))/2.

Octal palindromes which are also primes.

Coloring a circuit with 4 colors.

Arkons: number of elementary maps with n-1 nodes.

Number of rooted maps with n edges on Klein bottle.

Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix.

The Sally sequence: the length of repetition avoided in A006345.

a(n) = (n+1) a(n-1) + (-1)^n.

a(n) = (n+2)*a(n-1) + (-1)^n.

Related to series-parallel networks.

Related to series-parallel networks.

Number of series-parallel networks with n labeled edges. Also called yoke-chains by Cayley and MacMahon.

Coefficients in expansion of Eisenstein series E_2 (also called E_1 or G_2).

Expansion of (phi(-q^3) * psi(q))^3 / (phi(-q) * psi(q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.

Expansion of a cusp form of weight 8 for Gamma_1(6).

Number of binary vectors of length n containing no singletons.

a(n) = 2*a(n-1) + a(n-2) - a(n-3) for n >= 3, starting with a(0) = 1, a(1) = 3, and a(2) = 6.

Number of distributive lattices; also number of paths with n turns when light is reflected from 4 glass plates.

Number of distributive lattices; also number of paths with n turns when light is reflected from 5 glass plates.

Number of distributive lattices; also number of paths with n turns when light is reflected from 6 glass plates.