Sequences

Number of partitions of n, with two kinds of 1, 2, 3 and 4.

Number of partitions of n, with three kinds of 1,2,3 and 4 and two kinds of 5,6,7,...

Generating function = Product_{m>=1} 1/(1 - x^m)^2; a(n) = number of partitions of n into parts of 2 kinds.

EULER transform of 3, 2, 2, 2, 2, 2, 2, 2, ...

Number of partitions of n, with three kinds of 1 and 2 and two kinds of 3,4,5,....

Number of partitions of n, with three kinds of 1,2 and 3 and two kinds of 4,5,6,....

Number of partitions of n into parts of 3 kinds.

Number of graphs with n nodes and floor(n(n-1)/4) edges.

Boustrophedon transform of triangular numbers 1,1,3,6,10,...

Number of disconnected graphs with n nodes.

pi(n), the number of primes <= n. Sometimes called PrimePi(n) to distinguish it from the number 3.14159...

Number of NP-equivalence classes of balanced Boolean functions of n variables.

Number of invertible Boolean functions of n variables: a(n) = (2^n)!.

Invertible Boolean functions of n variables.

Invertible Boolean functions of n variables.

Invertible Boolean functions of n variables.

Number of partitions of n in which no parts are multiples of 3.

Expansion of Product_{k >= 1} (1 - x^k)^4.

Expansion of Product_{n>=1} (1-x^n)^5.

Expansion of Product_{k >= 1} (1 - x^k)^6.

Expansion of Product_{n>=1} (1 - x^n)^7.

Expansion of Product (1 - x^k)^8 in powers of x.

Boustrophedon transform of 1 & primes: 1,2,3,5,7,...

Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...

Boustrophedon transform of 1,1,2,4,8,16,32,...

Expansion of Product_{k>=1} (1 - x^k)^12.

Boustrophedon transform of Catalan numbers 1, 1, 1, 2, 5, 14, ...

Boustrophedon transform of natural numbers, cf. A000027.

Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,...

Expansion of Product_{k>=1} (1 - x^k)^16.

Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement; also Dirichlet convolution of b_n=2^(n-1) with mu(n); also number of components of Mandelbrot set corresponding to Julia sets with an attractive n-cycle.

Number of compositions of n into 3 ordered relatively prime parts.

Number of compositions of n into 4 ordered relatively prime parts.

Number of compositions of n into 5 ordered relatively prime parts.

Boustrophedon transform (second version) of Fibonacci numbers 1,1,2,3,...

Boustrophedon transform of squares.

Boustrophedon transform of triangular numbers.

Boustrophedon transform of primes.

Expansion of bracket function.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n > 3, with a(0)=a(1)=a(2)=0, a(3)=1.

Expansion of bracket function.

Boustrophedon transform of partition numbers.

Boustrophedon transform of powers of 2.

Boustrophedon transform of Catalan numbers.

Boustrophedon transform of odd numbers.

No-3-in-line problem on n X n grid: total number of ways of placing 2n points on n X n grid so no 3 are in a line. No symmetries are taken into account.

Boustrophedon transform of sequence 1,1,0,0,0,0,...

Number of cyclic permutations of [n] with no i -> i+1 (mod n).

Related to cumulative height of rooted plane trees.

Number of n-step self-avoiding walks on cubic lattice ending at point with x=0.