Sequences

Number of labeled 2-trees with n nodes.

Number of labeled 3-trees with n nodes.

Line-labeled 2-trees with n nodes.

Number of free n-ominoes with cell centers determining n-2 space (proper dimension n-2).

Number of chiral n-ominoes in n-2 space.

Number of asymmetric n-ominoes in n-2 space.

Number of free orthoplex n-ominoes with cell centers determining n-2 space.

Number of chiral orthoplex n-ominoes in n-2 space.

Number of asymmetric orthoplex n-ominoes in n-2 space.

Triangle of coefficients of generating function of ternary rooted trees of height at most n.

Number of ternary rooted trees with n nodes and height at most 3.

Number of ternary rooted trees with n nodes and height at most 4.

Number of ternary rooted trees with n nodes and height at most 5.

Number of ternary rooted trees with n nodes and height at most 6.

Number of ternary rooted trees with n nodes and height at most 7.

Number of ternary rooted trees with n nodes and height at most 8.

Floor[concatenation of seven consecutive numbers from n to n+6 divided by 7].

Number of primes p between powers of 2, 2^n < p <= 2^(n+1).

Special connected numbers: minimal and maximal connected numbers (cf. A029827) of a given binary order, i.e., between two consecutive powers of 2.

Number of true prime powers whose binary order, ceiling(log_2(p^x)), is n.

Number of connected numbers (A029827) in the interval [2^(n-1)+1, 2^n].

Odd split numbers: have a nontrivial factorization n=ab with a and b coprime, so that L(a) + L(b) <= L(n), where L(x) = A029837(x) = ceiling(log_2(x)).

First differences of odd split numbers (A036382).

Number of odd split numbers (A036382) in the interval [2^(n-1), 2^n].

Number of split numbers (A036382) with binary order (A029837) n, i.e., those in interval [ 2^(n-1), 2^n ].

Number of prime powers (p^2, p^3, ...) <= 2^n.

Number of connected numbers (A029827) with binary order (A029837) <= n.

Number of odd split numbers (A036382) of which the binary order (A029837) is <= n, i.e., those which occur below 2^n.

Number of (odd and even) split numbers (A036382) below 2^n.

First differences of composite connected numbers (A029827).

a(n) = sum of order of a mod n, 0 < a < n, gcd(a, n) = 1.

Coefficients of cluster series for site percolation problem on triangular lattice with 1st and 2nd neighbor bonds.

Duplicate of A003201.

Coefficients of cluster series for site percolation problem on f.c.c. lattice with 1st and 2nd neighbor bonds.

Coefficients of cluster series for site percolation problem on b.c.c. lattice with 1st and 2nd neighbor bonds.

Coefficients of cluster series for site percolation problem on simple cubic lattice with 1st and 2nd neighbor bonds.

Coefficients of cluster series for site percolation problem on triangular lattice with 1st, 2nd and 3rd neighbor bonds.

Coefficients of cluster series for site percolation problem on square lattice with 1st, 2nd and 3rd neighbor bonds.

Duplicate of A003200.

Coefficients of cluster series for site percolation problem on f.c.c. lattice with 1st, 2nd and 3rd neighbor bonds.

Coefficients of cluster series for site percolation problem on b.c.c. lattice with 1st, 2nd and 3rd neighbor bonds.

Coefficients of cluster series for site percolation problem on simple cubic lattice with 1st, 2nd and 3rd neighbor bonds.

Number of equilateral triangles whose vertices (whether connected by lines or not) lie at intersection points resulting from drawing lines connecting every pair of vertices of a regular 3n-gon (and extending beyond the polygon).

a(n) = ceiling(n^2/5).

a(n) = ceiling(n^2/7).

a(n) = ceiling(n^2/8).

a(n) = ceiling(n^2/9).

a(n) = ceiling(n^2/10).

a(n) = ceiling(n^2/11).

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