Sequences

Erroneous version of A223911: Tiered orders on n nodes.

Number of directed site animals on hexagonal lattice.

Euclid numbers: 1 + product of the first n primes.

Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.

Number of Hamiltonian cycles in P_4 X P_n.

Number of Hamiltonian cycles in P_5 X P_{2n}.

Number of irreducible polyhedral graphs with n nodes.

Number of irreducible polyhedral graphs with n faces.

Number of minimal 3-polyhedra with n edges.

Number of distinct vertex-degree sequences of n-faced polyhedral graphs.

Number of quasi-orders with n elements.

Exponentiation of g.f. for rooted trees.

Numbers k such that phi(k) = phi(sigma(k)).

Number of alternating 4-signed permutations.

Number of mu-atoms of period n on continent of Mandelbrot set.

Non-seed mu-atoms of period n in Mandelbrot set.

Mu-molecules in Mandelbrot set whose seeds have period n.

In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.

Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A006877.

Number of primes with n digits.

Number of primes < 10^n.

Squarefree semiprimes: Numbers that are the product of two distinct primes.

Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.

Long period primes: the decimal expansion of 1/p has period p-1.

In the '3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.

Record highest point of trajectory before reaching 1 in '3x+1' problem, corresponding to starting values in A006884.

Kaprekar numbers: positive numbers n such that n = q+r and n^2 = q*10^m+r, for some m >= 1, q >= 0 and 0 <= r < 10^m, with n != 10^a, a >= 1.

Kaprekar triples: q such that q = x + y + z and q^3 = x*10^2n + y*10^n + z, where z < 10^n and n is the number of digits in q. q is not a power of 10 (except q=1).

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

Exponent of least power of 2 having n consecutive 0's in its decimal representation.

Decimal expansion of Feigenbaum bifurcation velocity.

Decimal expansion of Feigenbaum reduction parameter.

Representation as a sum of squares requires n squares with greedy algorithm.

Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.

Number of planted 3-trees of height < n.

Parenthesized one way gives the powers of 2: (1), (2), (1+3), ..., another way the powers of 3: (1), (2+1), (3+6), ....

a(n) is the number of hierarchical linear models on n labeled factors allowing 2-way interactions (but no higher order interactions); or the number of simple labeled graphs with nodes chosen from an n-set.

a(n) is the number of hierarchical linear models on n unlabeled factors allowing 2-way interactions (but no higher order interactions); or the number of unlabeled simple graphs with <= n nodes.

a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).

Numbers of the form 2^i or 3^j.

Log of g.f. for rooted trees.

Number of caskets of order n.

a(n) = (2n)! * Sum_{k=0..n} (-1)^k * binomial(n,k) / (n+k)!.

Number of triangle-free trivalent (or cubic) graphs with 2n labeled nodes.

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

Number of transitive relations on n labeled nodes.

a(n) is the sum of products of terms in all partitions of n.

Number of zeros in character table of symmetric group S_n.

Number of nonzero elements in the character table of the symmetric group S_n.

Theta series of laminated lattice LAMBDA_10.