Sequences

a(n) = binomial(4n,n).

Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n.

Weight of balanced ternary representation of n.

Molien series for 6-dimensional complex representation of double cover of J2.

Number of 3-regular (trivalent) labeled graphs on 2n vertices with multiple edges and loops allowed.

Number of 4-valent labeled graphs with n nodes.

Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed.

a(n) = C(floor(n/2 + 1/2))*C(floor(n/2 + 1)) where C(i) = Catalan numbers A000108.

Numbers n that are primitive solutions to n^2 = a^2 + b^2 + c^2 (a,b,c > 0).

Number of words of length n in a certain language.

3-perfect (triply perfect, tri-perfect, triperfect or sous-double) numbers: numbers such that the sum of the divisors of n is 3n.

a(n) = floor(tau*a(n-1)) + a(n-2) with a(0)=0 and a(1)=1.

G.f.: x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1).

Numbers whose ternary expansion contains no 1's.

a(n) = 5*a(n-2) - 2*a(n-4), with initial terms 0,1,1,3.

Numerators in a worst case of a Jacobi symbol algorithm.

Worst case of a Jacobi symbol algorithm.

Worst case of a Jacobi symbol algorithm.

a(n) = 2*a(n-1)^2 - 1, a(0) = 4, a(1) = 31.

a(n) = floor(tau*a(n-1)) + a(n-2) with a(0)=0 and a(1)=2.

a(n) = floor(phi*a(n-1)) + a(n-2) where phi is the golden ratio.

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

Product k^(2^(k-1)), k = 1..n.

a(n) = floor(tau*a(n-2)) + a(n-1) with a(0)=0 and a(1)=1.

a(n) = floor(phi*a(n-2)) + a(n-1) where phi is the golden ratio.

Pseudoperfect (or semiperfect) numbers k: some subset of the proper divisors of k sums to k.

Numbers whose base-3 representation contains no 2.

Lexicographically earliest increasing sequence of positive numbers that contains no 4-term arithmetic progression.

Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 6.

Lexicographically earliest increasing nonnegative sequence that contains no 4-term arithmetic progression.

Expansion of (1-x)*e^x/(2-e^x).

Number of 4-dimensional polytopes with n vertices.

a(n) = minimal integer m such that an m X m square contains non-overlapping squares of sides 1, ..., n (some values are only conjectures).

The nonnegative even numbers: a(n) = 2n.

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

Bruckman-Lucas pseudoprimes: k | (L_k - 1), where k is composite and L_k = Lucas numbers A000032.

Primes of the form k^2 + k + 41.

Imaginary quadratic fields with class number 2 (a finite sequence).

Cyclotomic fields with class number 1 (or with unique factorization).

Indices of prime Cullen numbers: numbers k such that k*2^k + 1 is prime.

Primes p such that the NSW number A002315((p-1)/2) is prime.

The coding-theoretic function A(n,8,5).

The coding-theoretic function A(n,8,6).

The coding-theoretic function A(n,8,7).

The coding-theoretic function A(n,10,6).

The coding-theoretic function A(n,10,7).

The coding-theoretic function A(n,10,8).

The coding-theoretic function A(n,12,7).

The coding-theoretic function A(n,12,8).

The coding-theoretic function A(n,12,9).