Sequences

Coordination sequence for D_8 lattice.

Crystal ball sequence for D_8 lattice.

a(n) = floor(n/5)*ceiling(n/5).

11-rough numbers: not divisible by 2, 3, 5 or 7.

13-rough numbers: positive integers that have no prime factors less than 13.

Smallest prime factor is >= 17.

Composite but smallest prime factor >= 17.

Number of orbits on points that are at n steps from the origin in the f.c.c. lattice.

Number of orbits on points that are at n steps from 0 in D_4 lattice.

Number of orbits on points that are at n steps from 0 in D_5 lattice.

Number of orbits on points that are at n steps from 0 in D_6 lattice.

Number of orbits on points that are at n steps from 0 in D_7 lattice.

Number of orbits on points that are at n steps from 0 in D_8 lattice.

Number of orbits on points that are at n steps from 0 in D_9 lattice.

Number of orbits on points that are at n steps from 0 in D_10 lattice.

Coordination sequence for D_9 lattice.

Crystal ball sequence for D_9 lattice.

Coordination sequence for D_10 lattice.

Crystal ball sequence for D_10 lattice.

4*(2n-1)!*H(2n), where H(n) = Sum 1/i are harmonic numbers.

floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5).

a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5)*floor((n+4)/5).

Coordination sequence for A_4 lattice.

Crystal ball sequence for A_4 lattice.

Coordination sequence for A_5 lattice.

Crystal ball sequence for A_5 lattice.

Coordination sequence for A_6 lattice.

Crystal ball sequence for A_6 lattice.

Coordination sequence for A_7 lattice.

Crystal ball sequence for A_7 lattice.

Coordination sequence for A_8 lattice.

Crystal ball sequence for A_8 lattice.

Coordination sequence for A_9 lattice.

Crystal ball sequence for A_9 lattice.

Coordination sequence for A_10 lattice.

Crystal ball sequence for A_10 lattice.

Coordination sequence for E_7 lattice.

Crystal ball sequence for E_7 lattice.

Coordination sequence for E_6 lattice.

Crystal ball sequence for E_6 lattice.

Coordination sequence for {E_6}* lattice.

Crystal ball sequence for {E_6}* lattice.

G-symmetric Costas arrays of order n that are inequivalent under dihedral group but are not given by the Welch construction.

Number of Costas arrays of order n, counting rotations and flips as distinct.

n-th derivative of x^(1/x) at x=1.

Triangle T(n,k) read by rows, giving number of graphs with n nodes (n >= 1) and k edges (0 <= k <= n(n-1)/2).

Minimal difference s(n) between beginning and end of n consecutive large primes (n-tuplet) permitted by divisibility considerations.

Theta series of Leech lattice.

Theta series of 16-dimensional Barnes-Wall lattice.

a(0) = 1, a(n) = 480*sigma_7(n).