Sequences

Triangle of expansions of powers of x in terms of Chebyshev polynomials T_n (x).

Triangle of coefficients of Chebyshev polynomials U_n(x).

Triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).

Irregular triangle read by rows: one half of the coefficients of the expansion of (2*x)^n in terms of Chebyshev T-polynomials.

Catalan triangle read by rows. Also triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).

Triangle of coefficients of Legendre polynomials P_n (x).

Triangle of coefficients of expansions of powers of x in terms of Legendre polynomials P_n(x) over common denominator.

Smallest number strictly greater than previous one which is the sum of squares of two previous distinct terms (a(1)=1, a(2)=2).

Smallest number that is sum of squares of distinct earlier terms.

Smallest number that is not the sum of squares of two distinct earlier terms.

Smallest number that is not the sum of squares of distinct earlier terms.

Smallest number that is sum of cubes of two distinct earlier terms.

Number of simple connected regular bipartite graphs with 2n nodes.

Number of simple regular bipartite graphs with 2n nodes.

Number of simple regular trivalent bipartite graphs with 2n nodes.

Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).

Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).

Number of divisors of prime(n)-1.

Number of divisors of p+1, p prime.

phi(p-1), as p runs through the primes.

a(n) = phi(prime(n)+1).

Sum of divisors of p-1, p prime.

Sum of divisors of p+1, p prime.

Number of distinct primes dividing p-1, where p = n-th prime.

Number of distinct primes dividing p+1 as p runs through the primes.

a(n+1) = a(n)/n if n|a(n) else a(n)*n, a(1) = 1.

Number of orbits on points that are at n steps from 0 in E_8 lattice.

a(n+1) = a(n)/n! if n! divides a(n) else a(n)*n!.

a(1)=1; for n >= 1, a(n+1) = lcm(a(n),n) / gcd(a(n),n).

Coordination sequence for E_8 lattice.

a(n)=1, a(n+1) = lcm(a(n),b(n)) / gcd(a(n),b(n)), where {b(n)} = {fibonacci(n)}.

Minimal number of shift, add and subtract operations to multiply by n.

a(1)=1; thereafter a(n+1) = a(n)-n if a(n) >= n otherwise a(n+1) = a(n)+n.

a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.

a(n+1) = a(n)-b(n+1) if a(n) >= b(n+1) else a(n)+b(n+1), where {b(n)} are the triangular numbers A000217.

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

a(n) = Sum_{i=0..n-1} (-1)^i * prime(n-i).

a(0)=0; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n).

Crystal ball sequence for E_8 lattice.

Number of orbits of norm 2n vectors in E_8 lattice.

a(n) is the concatenation of a(n-1) and a(n-2) with a(1)=1, a(2)=2.

a(n) is formed by concatenating a(n-2) and a(n-1), with a(0) = 1, a(1) = 2.

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

a(n) = (5*n^2 + 1)*n^2 / 6.

Coordination sequence for D_5 lattice.

Crystal ball sequence for D_5 lattice.

Coordination sequence for D_6 lattice.

Crystal ball sequence for D_6 lattice.

Coordination sequence for D_7 lattice.

Crystal ball sequence for D_7 lattice.