Sequences

Generalized Fibonacci numbers D_{n,2}.

Generalized Fibonacci numbers D_{n,3}.

Number of down-up permutations of n+3 starting with n+1.

Number of down-up permutations of n+4 starting with n+1.

Number of down-up permutations of n+5 starting with n+1.

Number of down-up permutations of n+6 starting with n+1.

Number of down-up permutations of n+4 starting with 4.

Number of down-up permutations of n+5 starting with 5.

a(n) = Sum_{k=1..n} floor(n/k); also Sum_{k=1..n} d(k), where d = number of divisors (A000005); also number of solutions to x*y = z with 1 <= x,y,z <= n.

From descending subsequences of permutations.

From descending subsequences of permutations.

From Apery continued fraction for zeta(3): zeta(3)=6/(5-1^6/(117-2^6/(535-3^6/(1463...)))).

11*n^2 + 11*n + 3.

Number of binary rooted trees of height n requiring 3 registers.

Rabbytes: group eight successive Fibonacci numbers in binary and translate to decimal.

Rabbytes: group eight successive Fibonacci numbers in reversed binary and translate to decimal.

Number of abstract n-dimensional crystallographic point groups.

Number of n-dimensional space groups (including enantiomorphs).

Expansion of e.g.f. exp(arcsin(x)).

Expansion of e.g.f. exp( tan x ).

Bitriangular permutations.

a(n) = Sum_{k=2..n} n(n-1)...(n-k+1)/k.

Numerators of Cauchy numbers of first type.

Denominators of Cauchy numbers of first type.

a(n) = n*3^(n-4).

Complexity of doubled cycle (regarding case n = 2 as a multigraph).

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

Complexity of tensor sum of n graphs; or spanning trees on n-cube.

Complexity of (or spanning trees in) a 3 X n grid.

Row 3 of array in A212801.

Row 4 of array in A212801.

Number of minimal plane trees with n terminal nodes.

Extracting a square root.

Extracting a square root.

Hexagonal numbers (A000384) which are also centered hexagonal numbers (A003215).

Number of primitive sorting networks on n elements; also number of rhombic tilings of a 2n-gon.

Number of simple arrangements of pseudolines in the projective plane with an oriented marked cell; number of oriented abstract order types of n points (distinguishing mirror-symmetric copies).

Number of simple arrangements of n pseudolines in the projective plane with a marked cell. Number of Euclidean pseudo-order types: nondegenerate abstract order types of configurations of n points in the plane.

Number of projective pseudo order types: simple arrangements of pseudo-lines in the projective plane.

Number of hypertournaments on n elements under preisomorphism.

Number of hypertournaments on n elements under signed bijection.

Number of n-element posets which are unions of 2 chains.

Expansion of e.g.f. 1/(1 - log(1+x)).

Number of perfect matchings (or domino tilings) in C_4 X P_n.

Numbers k such that 2k-1 is prime.

R. L. Graham's sequence: a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1*b_2*...*b_t is a perfect square.

a(n) = Sum_{k=0..n} binomial(3*k,k)*binomial(3*n-3*k,n-k).

Josephus problem: a(2*n) = 2*a(n)-1, a(2*n+1) = 2*a(n)+1.

Numerators of approximations to e.

Denominators of approximations to e.