Sequences

Flimsy numbers.

Product of exponents of prime factorization of n.

Hoggatt sequence with parameter d=4.

Hoggatt sequence with parameter d=5.

Hoggatt sequence with parameter d=6.

Hoggatt sequence with parameter d=7.

Hoggatt sequence with parameter d=8.

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

Occurrences of principal character.

a(n) = 1 if n is of the form m(m+1), else 0.

a(n) = Fibonacci(Fibonacci(n+1) + 1).

a(n) = L(L(n)), where L(n) are Lucas numbers A000032.

a(n) = L(L(n+1)+1), where L(n) are Lucas numbers A000032.

A class of rooted trees with n nodes.

Hofstadter H-sequence: a(n) = n - a(a(a(n-1))).

a(0) = 0; a(n) = n - a(a(a(a(n-1)))) for n > 0.

a(n) = n - a(a(a(a(a(n-1))))).

Number of low discrepancy sequences in base 4.

The female of a pair of recurrences.

The male of a pair of recurrences.

Expansion of 1 / Product_{k>=1} (1-x^k)^(k+1).

Numbers k such that k and k-1 are composite.

Primes p such that 2p-1 is also prime.

Primes p such that (p+1)/2 is prime.

Sophie Germain primes p: 2p+1 is also prime.

Safe primes p: (p-1)/2 is also prime.

Area of n-th triple of squares around a triangle.

Number of partitional matroids on n elements.

Number of degree-n permutations of order a power of 2.

Number of Hamiltonian circuits on 2n times 4 rectangle.

Number of Hamiltonian circuits on 2n X 6 rectangle.

Number of Hamiltonian circuits on 2n X 8 rectangle.

Coefficients of high-temperature series for specific heat of spin-1/2 Ising model on a cristobalite lattice.

Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded down.

Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded to nearest integer.

Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded up.

Number of 2n-step polygons on honeycomb.

Number of n-step polygons on Kagome lattice.

Number of n-step polygons on f.c.c. lattice.

E.g.f.: high-temperature series in J/2kT for ferromagnetic susceptibility for the spin-1/2 Heisenberg model on hexagonal lattice.

High temperature series for spin-1/2 Heisenberg specific heat on 2D hexagonal lattice.

High-temperature series for Heisenberg model susceptibility on square lattice.

High temperature series for spin-1/2 Heisenberg specific heat on 2D square lattice.

Number of protruded partitions of n with largest part at most 2.

Number of protruded partitions of n with largest part at most 3.

Number of protruded partitions of n with largest part at most 4.

Number of protruded partitions of n with largest part at most 5.

Number of protruded partitions of n with largest part at most 6.

The odd numbers: a(n) = 2*n + 1.

Number of polynomials of height n: a(1)=1, a(2)=1, a(3)=4, a(n) = 2*a(n-1) + a(n-2) + 2 for n >= 4.