Sequences

a(n) = a(n-1) + a(n-2) with a(0)=2, a(1)=5. Sometimes called the Evangelist Sequence.

1-, 2-, 3-, ... digit numbers in alphabetical order in German.

1-, 2-, 3- ... digit numbers in alphabetical order in French (incorrect version, see A187876 for the correct version).

E.g.f. satisfies A'(x) = A(x/(1-x)).

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

Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.

Dimensions (sorted, with duplicates removed) of real simple Lie algebras.

Numerator of Bernoulli(2*n)/(2*n).

a(n) = floor(5*n/4), numbers that are congruent to {0, 1, 2, 3} mod 5.

Log2*(n) (version 2): take log_2 of n this many times to get a number < 2.

Number of normalized Latin squares with second row even.

Number of one-sided chessboard polyominoes with n cells.

Number of minimally 2-edge-connected non-isomorphic graphs with n nodes.

Label a 1-cm ruler with digits 1 cm wide.

Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^3/m) != 0.

a(0) = 1, a(1) = 2, a(n) = 4*a(n-1) - a(n-2).

Denominators of continued fraction convergents to sqrt(5).

Numerators of continued fraction convergents to sqrt(5).

a(n) = 10*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.

a(n) = 10*a(n-1) - a(n-2); a(0) = 1, a(1) = 5.

a(n) = 16*a(n-1) - a(n-2) with a(0) = 0, a(1) = 3.

a(n) = 16*a(n-1) - a(n-2).

Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, ...

Length of one version of Kolakoski sequence {A000002(i)} at n-th growth stage.

a(n) = 20*a(n-1) - a(n-2) with a(0) = 0, a(1) = 3.

a(n) = 20*a(n-1) - a(n-2).

Continued fraction associated with y(y+1) = x(x^2 -1).

Related to S(n), the number of self-dual monotone Boolean functions of n variables (A001206): 2^n-th term is S(n).

Product of totient function: a(n) = Product_{k=1..n} phi(k) (cf. A000010).

Number of permutations of [n] containing exactly 2 increasing subsequences of length 3.

a(n) = 8*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.

a(n) = 8*a(n-1) - a(n-2); a(0) = 1, a(1) = 4.

Union of all numbers {p, q} where p and q are both primes or powers of primes and q = p+2.

a(n) = n^3 + 1.

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

a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4).

a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5).

Twin primes.

Multiply previous term by 2 and write in binary.

a(n) = n^n - a(n-1), with a(1) = 1.

Triangle read by rows: T(n,k) = number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1.

Moran numbers: k such that k/(sum of digits of k) is prime.

Numbers k such that k / (sum of digits of k) is a square.

Numbers k such that (k / product of digits of k) is 1 or a prime.

Numbers n such that n / product of digits of n is a square.

a(n) = 2*n^2.

9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.

10-gonal (or decagonal) numbers: a(n) = n*(4*n-3).

a(n)-th triangular number is a square: a(n+1) = 6*a(n) - a(n-1) + 2, with a(0) = 0, a(1) = 1.

a(n)^2 is a triangular number: a(n) = 6*a(n-1) - a(n-2) with a(0)=0, a(1)=1.