Sequences

Numbers that are the sum of 4 positive 6th powers.

Numbers that are the sum of 5 positive 6th powers.

Numbers that are the sum of 6 positive 6th powers.

Numbers that are the sum of 7 positive 6th powers.

Numbers that are the sum of 8 positive 6th powers.

Numbers that are the sum of 9 positive 6th powers.

Numbers that are the sum of 10 positive 6th powers.

Numbers that are the sum of 11 positive 6th powers.

Numbers that are the sum of 12 positive 6th powers.

Numbers that are the sum of 2 positive 7th powers.

Numbers that are the sum of 3 positive 7th powers.

Numbers that are the sum of 4 positive 7th powers.

Numbers that are the sum of 5 positive 7th powers.

Numbers that are the sum of 6 positive 7th powers.

Numbers that are the sum of 7 positive 7th powers.

Numbers that are the sum of 8 positive 7th powers.

Numbers that are the sum of 9 positive 7th powers.

Numbers that are the sum of 10 positive 7th powers.

Numbers that are the sum of 11 positive 7th powers.

Numbers that are the sum of 12 positive 7th powers.

Numbers that are the sum of 2 nonzero 8th powers.

Numbers that are the sum of 3 nonzero 8th powers.

Numbers that are the sum of 4 nonzero 8th powers.

Numbers that are the sum of 5 nonzero 8th powers.

Numbers that are the sum of 6 nonzero 8th powers.

Numbers that are the sum of 7 nonzero 8th powers.

Numbers that are the sum of 8 nonzero 8th powers.

Numbers that are the sum of 9 nonzero 8th powers.

Sum of 10 nonzero 8th powers.

Numbers that are the sum of 11 positive 8th powers.

Sum of 12 nonzero 8th powers.

Numbers that are the sum of 2 positive 9th powers.

Numbers that are the sum of 3 positive 9th powers.

Numbers that are the sum of 4 positive 9th powers.

Numbers that are the sum of 5 positive 9th powers.

Numbers that are the sum of 6 positive 9th powers.

Numbers that are the sum of 7 positive 9th powers.

Numbers that are the sum of 8 positive 9th powers.

Numbers that are the sum of 9 positive 9th powers.

Sum of 10 positive 9th powers.

Number of asymmetric (not necessarily connected) graphs with n nodes.

Numbers of edges of regular polygons constructible with ruler (or, more precisely, an unmarked straightedge) and compass.

G.f.: 1/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^5)).

G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).

Number of solid partitions of n supported on graph of cube.

G.f.: (1 + x^4 + x^7 + 2*x^8 + x^9 + x^12 + x^16)/Product_{i=1..8} (1 - x^i).

Expansion of Ramanujan's function R(x) = 1 + Sum_{n >= 1} { x^(n*(n+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^n)) }.

Number of permutations of [n] with no 3-term arithmetic progression.

a(n) = binomial(3n+6, n).

a(n) = 3*binomial(2n-1,n).