Sequences

(A038590-1)/6.

Numbers missing from A038161.

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

Expansion of 1/((1-x)*(1-x^2))^4.

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

G.f.: 1/((1-x)*(1-x^2))^6.

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

Number of "connected animals" formed from n tricapped truncated tetrahedra in the diamond lattice, allowing translation and rotations of the lattice.

Number of "connected animals" formed from n triakis truncated tetrahedra connected along hexagonal faces in the triakis truncated tetrahedral honeycomb, allowing translations, rotations, and reflections of the honeycomb.

Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner-connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice.

Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice.

Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice and reflections.

Number of "polyspheres", or "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the f.c.c. lattice, allowing translation and rotations of the lattice, reflections and 180 deg. rotations about a 3-fold symmetry axis of the lattice.

Unbranched mono-5-catapolyheptagons.

A038175/2.

Number of unbranched mono-5-catapolyheptagons.

Numbers k such that k = (sum of digits of k)^(number of digits of k).

Result of second stage of sieve of Eratosthenes (after eliminating multiples of 2 and 3).

Number of "connected animals" formed from n square- or hexagon-connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice.

Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

3-infinitary perfect numbers k: 3-i-sigma(k) = 2*k, where 3-i-sigma = A049418.

One-dimensional cellular automaton 'sigma-minus' (Rule 90): 000,001,010,011,100,101,110,111 -> 0,1,0,1,1,0,1,0.

State of one-dimensional cellular automaton 'sigma' (Rule 150): 000,001,010,011,100,101,110,111 -> 0,1,1,0,1,0,0,1 at generation n, converted to a decimal number.

One-dimensional cellular automaton 'sigma' (Rule 150).

Numbers divisible by the sum and product of their digits.

Numbers other than powers of 10 that are coprime to the sum of their digits.

Smallest integer whose name in colloquial American English (no "and"s) uses n different letters.

Bit to left of least significant 1-bit in binary expansion of n.

Pagoda sequence: a(0) = b(n)-b(n-2) mod 3, where b(n) = A038189(n).

A034166/2.

Bisection of A001317.

Let G be an n-node graph with valencies d_1 .. d_n say; let m = (d_1 + ... + d_n)/n and s = n*Sum( (d_i-m)^2 ) be the scaled degree variance; a(n) gives number of different values taken by s.

Iterated sum-of-digits of n-th prime; or digital root of n-th prime; or n-th prime modulo 9.

Triangle read by rows: T(n,k) (n >= 2, 0 <= k <= n) = number of over-all crude totals of unbranched k-5-catapolyheptagons.

3-wave sequence starting with 1, 1, 1.

4-wave sequence.

Numbers k such that k^2 + 7 is a power of 2.

Row sums of triangle T(m,n) = number of solutions to 1 <= a(1) < a(2) < ... < a(m) <= n, where gcd(a(1), a(2), ..., a(m), n) = 1, in A020921.

Row sums of triangle K(m, n), inverse to triangle T(m,n) in A020921.

5-wave sequence.

Least k such that n! + k^2 is a square.

Number of distinct values of factorials mod n.

Least k such that factorials have exactly n distinct residues mod k.

Number of derangements of n where minimal cycle size is at least 3.

Can express a(n) with the digits of a(n)^2 in order, only adding plus signs.

Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).

Triangle whose (i,j)-th entry is binomial(i,j)*2^i.

Can express a(n) with the digits of a(n)^3 in order, only adding plus signs.

Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j)*4^j.