Sequences

a(n) = |a(n-1) + 2a(n-2) - n|.

Record values in A005210.

a(n) = n! if n is odd otherwise 0 (from the Taylor series for sin x).

Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1).

Triangular numbers together with squares (excluding 0).

Number of labeled interval graphs with n nodes.

Number of unlabeled identity interval graphs with n nodes.

Number of unlabeled unit interval graphs with n nodes.

Number of unlabeled reduced unit interval graphs on n nodes.

Number of unlabeled identity unit interval graphs.

Number of Dyck paths of knight moves.

Number of Dyck paths of knight moves.

Number of Dyck paths of knight moves.

Number of Dyck paths of knight moves.

T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence).

Number of permutations of length n with equal cycles.

Number of atomic species of degree n; also number of connected permutation groups of degree n.

Number of atomic species of degree n which are not nontrivial substitutions.

Sequence and first differences (A030124) together list all positive numbers exactly once.

a(1) = a(2) = 1; for n > 2, a(n) = a(a(n-2)) + a(n - a(n-2)).

Stern's sequence: a(1) = 1, a(n+1) is the sum of the m preceding terms, where m*(m-1)/2 < n <= m*(m+1)/2 or equivalently m = ceiling((sqrt(8*n+1)-1)/2) = A002024(n).

Odd abundant numbers (odd numbers m whose sum of divisors exceeds 2m).

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

A finite sequence associated with the Lie algebra A_5.

Primes p such that 1 + product of primes up to p is prime.

Fortunate numbers: least m > 1 such that m + prime(n)# is prime, where p# denotes the product of all primes <= p.

Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n.

Numbers k such that k and k+1 have the same number of divisors.

Numbers k such that k, k+1 and k+2 have the same number of divisors.

Irregular triangle of Section I numbers. Row n contains numbers k with 2^n < k < 2^(n+1) and phi^n(k) = 2, where phi^n means n iterations of Euler's totient function.

P-positions in Epstein's Put or Take a Square game.

N-positions in Epstein's Put or Take a Square game.

A self-generating sequence.

A self-generating sequence: start with 1 and 2, take all sums of any number of successive previous elements and adjoin them to the sequence. Repeat!

A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence.

The (Mahler-Popken) complexity of n: minimal number of 1's required to build n using + and *.

a(n) = (1 + a(n-1)*a(n-2))/a(n-3), a(0) = a(1) = a(2) = 1.

a(n) = 3*a(n-2) - a(n-4), a(0)=2, a(1)=1, a(2)=3, a(3)=2. Alternates Lucas (A000032) and Fibonacci (A000045) sequences for even and odd n.

Bisection of Lucas numbers: a(n) = L(2*n) = A000032(2*n).

Determinant of inverse Hilbert matrix.

Record gaps between primes.

a(0) = 0, a(1) = a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).

a(n) = Sum_{k=0..floor(n/4)} binomial(n-2k,2k).

Number of binary words of length n in which the ones occur only in blocks of length at least 4.

Number of weighted voting procedures.

Atkinson-Negro-Santoro sequence: a(n+1) = 2*a(n) - a(n-floor(n/2+1)).

Number of weighted voting procedures.

Number of weighted voting procedures.

Apéry numbers: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k).

Apery (Apéry) numbers: Sum_{k=0..n} (binomial(n,k)*binomial(n+k,k))^2.