Sequences

Mahonian statistics on S_n which split (a(n)=n!.a(n-1)^n).

Number of triangular numbers that divide n.

Number of hybrid binary trees with n internal nodes.

Number of matrix bundles of codimension n (Euler transform of A001156).

Number of sum-free subsets of {1, ..., n}.

Number of `homogenized' N-free graphs with n nodes.

Complementary pairs of `homogenized' N-free graphs with n nodes.

Number of inverse pairs of elements in symmetric group S_n, or pairs of total orders on n nodes (average of A000085 and A000142).

Number of complementary pairs of graphs on n nodes. Also number of unlabeled graphs with n nodes and an even number of edges.

Determinant of character table of symmetric group S_n.

Number of simple juggling patterns of n balls.

Sum of indices of windows of trapezoidal maps.

Indices of last windows of trapezoidal maps.

Distinct perimeter lengths of polygons with regularly spaced vertices.

Number of ways of writing n as p*q, with p <= q, gcd(p, q) = 1.

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

Period 4 zigzag sequence: repeat [0,1,2,1].

Number of terms in discriminant of generic polynomial of degree n.

Chimes made by clock striking the hour and half-hour.

Westminster chimes at 15-minute intervals (1).

Erroneous version of A001357 printed by mistake on back cover of Encyclopedia of Integer Sequences.

Number of lattice points inside circle of radius n is 4(a(n)+n)-3.

Westminster chimes at 15-minute intervals (2).

Chimes made by clock striking quarter-hours.

Numbers n such that balanced sequences exist with n distinct elements.

Number of cycles induced by iterating the Gray-coding of an n-bit number: a(n+1) = a(n) + 2^n/C_n, where C_n = least power of 2 >= n (C_n is the length of the cycle), with a(0) = 1.

a(n) = Fibonacci(n) mod 9.

Euler characteristic of mapping class group Gamma_n.

Number of intransitive (or alternating, or Stanley) trees: vertices are [0,n] and for no i<j<k are both (i,j) and (j,k) edges.

Summarize the previous term! (in decreasing order).

A Kutz sequence.

A Kutz sequence.

A Kutz sequence.

Number of fullerenes with 2n vertices (or carbon atoms).

Number of terms in the Zeckendorf representation of n (write n as a sum of non-consecutive distinct Fibonacci numbers).

Psi_c(n), where Product_{k>1} 1/(1-1/k^s)^phi(k) = Sum_{k>0} psi_c(k)/k^s.

a(n) is multiplicative with a(2) = 1; a(4) = 2; a(2^i) = 2^(i-2)+2 if i>2; a(p^i) = 1+(p-1)*p^(i-1)/2 if prime p>2 and i>0.

a(n) = psi_c(n), where Product_{k>1} 1/(1-1/k^s)^A007897(k) = Sum_{k>0} psi_c(k)/k^s.

Coordination sequence for hexagonal close-packing.

Coordination sequence for D_4 lattice.

Number of minimal unavoidable n-celled pebbling configurations.

Number of pebbling configurations with n pebbles.

The number of distinct principal ideals in the semigroup of binary relations on an n-set.

Crystal ball sequence for diamond.

Conflicts during insertions into exchange trees on n nodes.

Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.

Concatenation of sequence (1, 2, ..., floor((n-1)/2), floor(n/2), floor(n/2)-1, ..., 1) for n >= 1.

Triangle of the gods: to get a(n), concatenate the decimal numbers 1,2,3,...,n.

Expansion of (1-x)/(1-2*x+x^2-2*x^3).

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