Sequences

Number of partitions of n into distinct squares.

Exponential (or "EXP") transform of squares A000290.

EXPCONV of squares A000290 with themselves.

Logarithmic (or "LOG") transform of squares A000290.

Numerators of the first differences of 1/(n^2 + 1).

Denominators of the first differences of 1/(n^2 + 1).

Partial sums of sequence {1/(i^2+1): i=0..n} (numerators).

Partial sums of sequence {1/(i^2+1): i=0..n} (denominators).

Denominator of Bernoulli(2n,1/2).

Numerator of Bernoulli(2n,1/3).

Denominator of Bernoulli(2n,1/3).

Number of n-vertex labeled graphs that are gracefully labeled trees.

Numerator of (2*n+1)!*8*Bernoulli(2*n,1/2).

Duplicate of A001896.

Denominator of Bernoulli(2n,1/4).

Squares of primes or products of pairs of consecutive primes.

Products p^3 or p^2*q, where {p,q} are consecutive primes.

3x+1 sequence beginning at 3.

3x+1 sequence beginning at 9.

3x + 1 sequence beginning at 15.

3x+1 sequence beginning at 21.

Expansion of (1+2*x-3*x^2-4*x^3+x^4)/(1-8*x^2+11*x^4).

Number of disconnected 4-valent (or quartic) graphs with n nodes.

a(n) = 3*2^n - 2.

a(n) = a(n-1) + a(floor(n/2)), a(1) = 1.

a(n) = n*(n + 1)*(n + 2)*(n + 3)/2.

a(n) = n*(n+1)*(n+2)*(n+3)/4.

a(n) = n*(n+1)*(n+2)*(n+3)/6.

a(1) = 1, a(n) = 2*a(n-1) + a([n/2]).

a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2.

a(n) is the smallest integer that takes n halving and tripling steps to reach 1 in the 3x+1 problem.

Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A006877 (same as A006878 except here we start counting at 1 instead of 0).

Sum of the numbers in the trajectory of n for the 3x+1 problem.

Record sum of numbers in trajectory of 3x+1 problem.

Initial number for record sum of numbers in trajectory of 3x+1 problem.

Numbers m that are the largest number in their Collatz (3x+1) trajectory.

a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2, a(3) = 4.

a(n) = a(n-1)+ a(round(2*(n-1)/3)) +a(round((n-1)/3)) starting a(1)=1.

a(n) = a(n-1) + a(round(2*(n-1)/3)) + a(round((n-1)/3)) with a(1)=a(2)=1.

a(n) = a(n-1) + a(round(2*(n-1)/3)) + a(round((n-1)/3)) with a(1)=1, a(2)=2.

Almost-squares: m such that m/p(m) >= k/p(k) for all k<m, where p(m) is the least perimeter of a rectangle with integer side lengths and area m.

Carmichael numbers of the form (6*k+1)*(12*k+1)*(18*k+1), where 6*k+1, 12*k+1 and 18*k+1 are all primes.

First differences of A046025.

a(n)/4^n is the expected number of tosses of a coin required to obtain n+1 heads or n+1 tails.

Expansion of 1/(1 - 3*x - x^2 + x^3).

Number of matchings in graph P_{3} X P_{n}.

Number of matchings in graph P_{4} X P_{n}.

Number of matchings in graph P_{5} X P_{n}.

Number of matchings in graph P_{6} X P_{n}.

Number of matchings in graph P_{7} X P_{n}.