Sequences

Pisot sequences E(5,7), P(5,7).

Pisot sequences E(5,8), P(5,8).

Pisot sequences E(5,9), P(5,9).

a(n) = 5 * 2^n.

a(n) = n + 6.

Pisot sequences E(6,8), P(6,8).

Pisot sequences L(6,9), E(6,9).

Pisot sequences E(6,10), P(6,10).

a(n) = n + 7.

Pisot sequences E(7,9), P(7,9).

Pisot sequences E(7,10), P(7,10).

a(n) = n + 8.

a(n) = n + 9.

G.f.: 1/((1-6*x)*(1-9*x)*(1-12*x)).

Integers >= 2. a(n) = n+1.

Expansion of g.f. 1/((1-6*x)*(1-10*x)*(1-11*x)).

Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1).

Pisot sequence T(2,9), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequences E(2,10), L(2,10), P(2,10), T(2,10).

Pisot sequences L(3,7) or S(3,7).

Numbers n for which number of distinct prime divisors of C(n,k) has maximum at k = [n/2].

Pisot sequence T(4,7).

Consider number of prime divisors of binomial(n,k), k=0..n; a(n) = multiplicity of the maximum value.

Pisot sequence L(4,10).

Odd numbers >= 5.

Pisot sequence L(5,8).

Pisot sequence L(5,9).

Consider number of divisors of binomial(n, k), k=0..n; a(n) = multiplicity of the maximum value.

a(n) = 2*n + 6.

Max_{k=0..n} d(C(n,k)) - d(C(n,[ n/2 ])), where d() = number of divisors.

Pisot sequence T(6,10), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(7,9).

Pisot sequence L(7,10).

Pisot sequences P(8,10), T(8,10).

Pisot sequence T(3,5).

Pisot sequence T(3,7), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(4,6), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(4,10), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(5,8), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(5,9), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(6,9), a(n) = floor(a(n-1)^2/a(n-2)).

Pisot sequence T(7,10), a(n) = floor(a(n-1)^2/a(n-2)).

Sizes of successive increasing gaps between squarefree numbers.

Increasing gaps between squarefree numbers (lower end).

Increasing gaps between squarefree numbers (upper end).

Numbers that are the sum of two triangular numbers.

Numbers that are not the sum of two triangular numbers.

Expansion of 1/((1-6x)(1-10x)(1-12x)).

Decimal expansion of (-1)*Gamma'(1/2)/Gamma(1/2) where Gamma(x) denotes the Gamma function.

Decimal expansion of 1/sqrt(3).