A golden example (formula (34) here)

A BBPP (for BBP+Pochhammer) formula for Pi (formula (57) here)

A double series for zeta(2) (formula (8) here)

A limit formula for log(2) involving all zeta numbers (formula (129) here)

A formula for zeta(3) rediscovered (formula (10) here)

A series for log(2) (formula (45) here)

An identity for generalised harmonic numbers H(n,2) (formula (33) here)

A limit formula for the gamma constant (formula (36) here)

A false Lehmer cotengent expansion for Phi (formula (4) here)

Asymptotic formula for Motzkin numbers

Bisection of Fibonacci numbers

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-4).

Asymptotic formula for 3-smooth numbers

Central trinomial coefficients

Numbers n such that 2*n^2 - 1 is a square

n-th number without consecutive equal binary digits

Number of graphs on n unlabeled nodes

Number of partitions of n into at most 3 parts

The multiplicative partition function

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

Asymptotic for number of necklaces of partitions of n+1 labeled beads

Conjectured formula for the least k such that H(k)>n

Genocchi numbers of first kind

Pillai's arithmetical function: sum of gcd(k, n) for 1 = k = n

Number of ways of writing n as a sum of 4 squares

Number of elements in the set {(x,y): 1=x,y=n, gcd(x,y)=1}

Number of (positive) squarefree numbers n

Numbers whose ternary expansion contains no 1's

a(n) = least k such that n divides Fibonacci number F_k

Denominators of Farey tree fractions

Regular paper-folding sequence

Number of ternary (0,1,2) sequences without a consecutive '012'

Number of combinations of n things from 1 to n at a time, with repeats allowed

Number of cyclic subgroups of the group C_n X C_n (where C_n is the cyclic group of order n)

Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 2

Numerator of tan(2n arctan(1/2))

Denominator of tan(2n arctan(1/2))

Number of n X n matrices with nonnegative entries and every row and column sum 2.

Unique monotonic sequence of nonnegative integers satisfying a(a(n)) = 3n

Number of paths with n turns when light is reflected from 5 glass plates

Number of minimax trees on n nodes