Sequences

Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents.

Number of acyclic disubstituted alkanes with n carbon atoms and identical substituents.

Number of carbon trees with n carbon atoms.

Number of restricted hexagonal polyominoes with n cells.

Number of trivalent connected (or cubic) planar graphs with 2n nodes.

Erroneous version of A000421.

Number of trivalent planar loopless multigraphs with 2n nodes.

Number of isomorphism classes of connected 3-regular multigraphs of order 2n, loops allowed.

Sum of cubes of first n Fibonacci numbers.

Sum of fourth powers of Fibonacci numbers.

Partial sums of squares of Lucas numbers.

Partial sums of cubes of Lucas numbers.

Partial sums of fourth powers of Lucas numbers.

Number of connected labeled interval graphs with n nodes.

Number of unlabeled connected identity interval graphs with n nodes.

Number of interval graphs on n unlabeled nodes.

Number of unlabeled connected interval graphs with n nodes.

Reduced interval graphs with n nodes.

Number of dependable interval graphs with n nodes.

Number of Hamiltonian rooted triangulations with n internal nodes and 5 external nodes.

Let F(x) = 1 + x + 4x^2 + 9x^3 + ... = g.f. for A002835 (solid partitions restricted to two planes) and expand (1-x)*(1-x^2)*(1-x^3)*...*F(x) in powers of x.

Number of 2 up, 2 down, 2 up, ... permutations of length 2n + 1.

3 up, 3 down, 3 up, ... permutations of length 3n+1.

Number of 4 up, 4 down, 4 up, ... permutations of length 4n+1.

Related to recurrences over rings.

Length of longest trail (i.e., path with all distinct edges) on the edges of an n-cube.

Number of column-strict plane partitions of n.

Number of symmetric plane partitions of n.

x^3 + n*y^3 = 1 is solvable.

Values B(2,n)/4 of Gandhi polynomials defined by B(x,0)=x and B(x,n) = x^2 (B(x+1,n-1) - B(x,n-1)).

a(n) = (n-1)*(n+1)!/6.

a(n) is the index of the last occurrence of the n-th distinct term (equal to n+1) in sequence A155934(m) = k(m) = the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros.

Erroneous version of A011260.

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

Alkane (or paraffin) numbers l(7,n).

Alkane (or paraffin) numbers l(8,n).

G.f.: 2*(1-x^3)/((1-x)^5*(1+x)^2).

Number of paraffins.

Number of paraffins.

Number of paraffins.

a(n) = (n+1)*(n^2+n+2)/2; g.f.: (1 + 2*x^2) / (1 - x)^4.

Number of paraffins.

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

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

a(n) = C(n+2,3) + C(n,3) + C(n-1,3).

The odd prime numbers together with 1.

Weight distribution of [ 128,29,32 ] 2nd-order Reed-Muller code.

4-dimensional analog of centered polygonal numbers: a(n) = n(n+1)*(n^2+n+4)/12.

Number of inequivalent ways to color vertices of a regular tetrahedron using <= n colors.

Number of paraffins.