Sequences

Triangular array formed from elements to right of middle of rows of Pascal's triangle that are not 1.

Inverse of 403rd cyclotomic polynomial.

Triangular array formed from elements to right of middle of Pascal's triangle.

Odd elements in Pascal's triangle that are not 1.

Inverse of 406th cyclotomic polynomial.

Inverse of 407th cyclotomic polynomial.

Representation of n in base of Fibonacci numbers (the Zeckendorf representation of n). Also, binary words starting with 1 not containing 11, with the word 0 added.

Representation of n in base of Catalan numbers (a classic greedy version).

Write n in base of Catalan numbers, then interpret as if written in base 3.

Minimal number of Catalan numbers that sum to n.

Odd elements in Pascal's triangle.

Inverse of 413th cyclotomic polynomial.

From table of maximal epacts e(p) and corresponding primes p, for x_1=2, x_{m+1} = (x_m)^2+1; sequence gives e(p).

From table of maximal epacts e(p) and corresponding primes p, for x_1=2, x_{m+1} = (x_m)^2+1; sequence gives p.

From table of maximal epacts e(p) and corresponding primes p, for x_0=2, x_{m+1} = (x_m)^2-1; sequence gives e(p).

From table of maximal epacts e(p) and corresponding primes p, for x_0=2, x_{m+1} = (x_m)^2-1; sequence gives p.

Inverse of 418th cyclotomic polynomial.

Even elements in Pascal's triangle.

Inverse of 420th cyclotomic polynomial.

Subtract 1 from Pascal's triangle, read by rows.

a(1) = 1, a(2) = 2, a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

a(n) = Sum_{i=1..n-1} a(i)*a(n-1-i), with a(0) = 1, a(1) = 3.

a(n) = Sum_{i=0..n-1} a(i)*a(n-i), with a(0) = 1 and a(1) = 4.

a(n) = Sum_{i=0..n-1} a(i) * a(n-i), a(0) = 1, a(1) = 5.

a(n) = Sum_{i=0..n-1} a(i)*a(n-i) with a(0)=1, a(1)=6.

Inverse of 427th cyclotomic polynomial.

Odd Fibonacci numbers.

Inverse of 429th cyclotomic polynomial.

Differences between two positive cubes in exactly 1 way.

Differences between two positive cubes in exactly 2 ways.

Differences between two positive cubes in exactly 3 ways.

Largest prime factor of n^2 + 1.

Inverse of 434th cyclotomic polynomial.

Inverse of 435th cyclotomic polynomial.

Even Fibonacci numbers; or, Fibonacci(3*n).

Inverse of 437th cyclotomic polynomial.

Odd Lucas numbers.

Even Lucas numbers: a(n) = L(3*n).

Numbers in the triangle of Eulerian numbers (A008292) that are not 1.

Even numbers in the triangle of Eulerian numbers.

Inverse of 442nd cyclotomic polynomial.

Theta series of quadratic form with Gram matrix [ 1, 0, 0; 0, 2, 1; 0, 1, 2 ].

Theta series of quadratic form with Gram matrix [ 2, 0, 0; 0, 2, 1; 0, 1, 2 ].

Sum_{1<=k<n} gcd(k!,n!/k!).

Theta series of quadratic form with Gram matrix [ 1, 0, 0; 0, 1, 0; 0, 0, 2 ]. Number of integer solutions to x^2 + y^2 + 2*z^2 = n.

Numbers represented by quadratic form with Gram matrix [ 2, 1, 0; 1, 3, 1; 0, 1, 2 ].

Theta series of quadratic form (or lattice) with Gram matrix [ 2, 1, 0; 1, 3, 1; 0, 1, 2 ].

Theta series of quadratic form with Gram matrix [ 2, 1, 0; 1, 4, 1; 0, 1, 2 ].

Odd numbers in the triangle of Eulerian numbers.

Inverse of 451st cyclotomic polynomial.