Sequences

Number of 4-unbalanced strings of length n (=2^n-A027559(n)).

Number of 5-unbalanced strings of length n (=2^n-A027560(n)).

Numbers not of form abc + abd + acd + bcd for 1<=a<=b<=c<=d.

Numbers not of form abcd + abce + abde + acde + bcde for 1 <= a <= b <= c <= d <= e.

Largest number not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i integers >= 1.

Number of numbers not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i >= 1.

Number of distinct (modulo rotation and reflection) n X n panmagic = pandiagonal = diabolic = Nasik squares.

Numbers that are both triangular and tetrahedral.

Initial members of prime decaplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26, p+30, p+32).

Initial members of prime decaplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30, p+32).

Numbers k such that k^2 + (k+1)^2 is palindromic.

Palindromes of form n^2 + (n+1)^2.

Numbers n such that n^2 + (n+1)^2 + (n+2)^2 is palindromic.

Palindromes of form n^2 + (n+1)^2 + (n+2)^2.

a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2.

Numbers n such that n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 is palindromic.

Palindromes of form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2.

Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.

Numbers n such that n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 is palindromic.

Palindromes of the form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.

Sequence satisfies T(T(a))=a, where T is defined below.

Sequence satisfies T(T(a))=a, where T is defined below.

Sequence satisfies T(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T^2(a)=a, where T is defined below.

Sequence satisfies T(a)=a, where T is defined below.

Numbers k such that the set of prime divisors of k is equal to the set of prime divisors of sigma(k).

a(n) = 3*n^2 - 7*n + 6.

Number of partitions of 4^n-1 into n-th powers.

Number of partitions of 4^n into n-th powers.

a(n) = n^3 + (n+1)^3 + (n+2)^3.

a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3.

a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3 + (n+4)^3.

Sum of two cubes in 4 ways involving at least one sum of coprime cubes.

e in duodecimal.

Number of non-well-founded sets or hypersets (sets that can contain themselves) of level n (representable by graphs with n nodes).

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

Least non-partition into positive n-th powers.

The number of Apollonian networks (planar 3-trees) with n+3 vertices.