Sequences

Boustrophedon transform of 1,1,2,3,4,5,...

Shifts 2 places left under boustrophedon transform.

Number of relations with 3 arguments on n nodes.

Number of relations on an infinite set.

Number of graphs with n edges.

Number of 3-uniform hypergraphs on n unlabeled nodes, or equivalently number of relations with 3 arguments on n nodes.

Number of symmetric relations on n nodes.

Boustrophedon transform of all-1's sequence.

Mersenne primes (primes of the form 2^n - 1).

Number of series-reduced planted trees with n leaves. Also the number of essentially series series-parallel networks with n edges; also the number of essentially parallel series-parallel networks with n edges.

Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].

Number of boron trees with n nodes, i.e. n-node rooted trees with degree <= 3 at root and out-degree <= 2 elsewhere.

Number of 3-valent trees (= boron trees or binary trees) with n nodes.

Number of bicentered 3-valent (or boron, or binary) trees with n nodes.

Boustrophedon transform of 1, 2, 2, 2, 2, ...

Number of centered 3-valent (or boron, or binary) trees with n nodes.

Number of centered trees with n nodes.

Number of bicentered trees with n nodes.

Number of carbon (rooted) trees with n carbon atoms = unordered 4-tuples of ternary trees.

Number of groups of order 2^n.

a(n) = (2n)!/2^n.

Number of n X n matrices with nonnegative entries and every row and column sum 2.

Semi-meanders: number of ways a semi-infinite directed curve can cross a straight line n times.

Number of colorings of labeled graphs on n nodes using exactly 2 colors, divided by 4.

Number of colored labeled n-node graphs with 2 interchangeable colors.

Number of 3-colored labeled graphs on n nodes, divided by 3.

Number of 4-colored labeled graphs on n nodes, divided by 4.

Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,...

Number of Abelian groups of order n; number of factorizations of n into prime powers.

Final decimal digit of 2^n.

Landau's approximation to population of x^2 + y^2 <= 2^n.

Ramanujan's approximation to population of x^2 + y^2 <= 2^n.

An approximation to population of x^2 + y^2 <= 2^n.

Related to population of numbers of form x^2 + y^2.

Related to population of numbers of form x^2 + y^2.

Moser-de Bruijn sequence: sums of distinct powers of 4.

Numbers k such that (1,k) is "good".

Boustrophedon transform of 1, 1, 4, 9, 16, ...

A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!.

Number of irreducible chord diagrams with 2n nodes.

Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes.

One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes.

a(n) is the number of conjugacy classes in the alternating group A_n.

Chromatic number (or Heawood number) of nonorientable surface with n crosscaps.

Number of degree-n even permutations of order dividing 2.

n-th superior highly composite number A002201(n) is product of first n terms of this sequence.

Expansion of modular function 1/E_3 (cf. A013973).

Number of permutations of [1,2,...,n] with n-1 inversions.

a(n) = E(n+1) - 2*E(n), where E(i) is the Euler number A000111(i).

Related to population of numbers of form x^2 + y^2.