Sequences

a(n) = a(n-1) + a(n-8), with a(i) = 1 for i = 0..7.

a(n) = a(n-1) + a(n-9) for n >= 9; a(n) = 1 for n=0..7; a(8) = 2.

Coefficient of x^4 in expansion of (1+x+x^2)^n.

Define strings S(0)=0, S(1)=11, S(n) = S(n-1)S(n-2); iterate.

Coefficient of x^6 in expansion of (1+x+x^2)^n.

Coefficient of x^7 in expansion of (1+x+x^2)^n.

Coefficient of x^8 in expansion of (1+x+x^2)^n.

Construct triangle in which n-th row is obtained by expanding (1 + x + x^2)^n and take the next-to-central column.

Quadrinomial coefficients: C(2+n,n) + C(3+n,n) + C(4+n,n).

Quadrinomial coefficients.

Quadrinomial coefficients.

Central quadrinomial coefficients.

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

Quadrinomial coefficients.

Quadrinomial coefficients.

Quadrinomial coefficients.

Quadrinomial coefficients.

n-th derivative of x^x at x=1. Also called Lehmer-Comtet numbers.

Number of fractions in Farey series of order n.

a(n) is the smallest positive integer a for which there is an identity of the form a*n*x = Sum_{i=1..m} ai*gi(x)^n where a1, ..., am are in Z and g1(x), ..., gm(x) are in Z[x].

Related to n-th powers of polynomials: factors complementary to A005731.

Related to n-th powers of polynomials: factors complementary to A005730.

a(n) = binomial(n+3,6) + binomial(n+1,5) + binomial(n,5).

Least k such that binomial(k,n) has n or more distinct prime factors.

Incomplete version of A001049.

Greatest k such that binomial(k,n) has fewer than n distinct prime factors.

Number of degenerate fanout-free Boolean functions of n variables using And, Or and Not gates.

Number of fanout-free Boolean functions of n variables using And, Or and Not gates.

Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates.

Number of disjunctively-realizable functions of n variables.

Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.

Number of fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.

Number of degenerate fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

Number of fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

Expansion of x*(1+x-x^2)/((1-x)^4*(1+x)).

Number of n-covers of an unlabeled 3-set.

Number of n-covers of an unlabeled 4-set.

Number of n-covers of an unlabeled 6-set.

Number of n-covers of an unlabeled 7-set.

Cascade-realizable Boolean functions of n variables.

Number of planted matched trees with n nodes.

Number of matched trees with 2n nodes.

a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2.

Number of rooted identity matched trees with n nodes.

Number of planted identity matched trees with n nodes.

Number of identity matched trees with n nodes.

Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 2.

Coefficients of modular function g_4(tau).

Number of partitions of n into parts of 12 kinds.

Coefficients of modular function g_6(tau).