Sequences

Number of symmetric ways of folding a strip of n labeled stamps.

Number of discordant permutations.

Number of discordant permutations.

Number of discordant permutations.

Number of discordant permutations.

Number of discordant permutations.

Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2.

Octagonal numbers: n*(3*n-2). Also called star numbers.

Number of outcomes of unlabeled n-team round-robin tournaments.

Number of graphical partitions of 2n.

Number of tournaments on n nodes determined by their score vectors.

Number of different score sequences that are possible in an n-team round-robin tournament.

A Beatty sequence: [ n(e+1) ].

Number of 4 X n normalized Latin rectangles.

Coefficient of x^5 in expansion of (1 + x + x^2)^n.

Tenth column of quintinomial coefficients.

a(n) is the number of (n-2) X n normalized Latin rectangles.

Number of triangular polyominoes (or triangular polyforms, or polyiamonds) with n cells (turning over is allowed, holes are allowed, must be connected along edges).

The cubes: a(n) = n^3.

Figurate numbers or binomial coefficients C(n,6).

a(n) = binomial coefficient C(n,7).

a(n) = binomial coefficient C(n,8).

a(n) = binomial coefficient C(n,9).

Fourth powers: a(n) = n^4.

Fifth powers: a(n) = n^5.

Number of equivalence classes of Boolean functions of n variables under GL(n,2).

Number of partitions of n into distinct primes.

Rao Uppuluri-Carpenter numbers (or complementary Bell numbers): e.g.f. = exp(1 - exp(x)).

a(n) = 7*binomial(2n,n-3)/(n+4).

a(n) = 11*binomial(2n,n-5)/(n+6).

a(n) = 13*binomial(2n,n-6)/(n+7).

Number of n-state 2-input 1-output automata with one initial and one terminal state.

Number of nonnegative solutions of x^2 + y^2 = z in first n shells.

Sum of odd divisors of n.

Ramanujan's tau function (or Ramanujan numbers, or tau numbers).

Number of binary relations on n unlabeled points.

Central factorial numbers: A008955(n,2).

Central factorial numbers: A008955(n,3).

Number of rooted ternary trees with n nodes; number of n-carbon alkyl radicals C(n)H(2n+1) ignoring stereoisomers.

Number of secondary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.

Number of tertiary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms.

Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).

Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers.

Number of nonnegative solutions to x^2 + y^2 <= n^2.

Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.

Number of points of norm <= n in cubic lattice.

Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.

Number of partitions of n into prime parts.

Number of connected partially ordered sets with n unlabeled elements.

Number of threshold functions of n or fewer variables.