Sequences

Coordination sequence for C_5 lattice.

Coordination sequence for C_6 lattice.

Coordination sequence for C_7 lattice.

Coordination sequence for C_8 lattice.

The squarefree numbers ordered lexicographically by their prime factorization (with factors written in decreasing order). a(n) = Product_{k in I} prime(k+1), where I is the set of indices of nonzero binary digits in n = Sum_{k in I} 2^k.

The differences 1-1, 21-12, 321-123, ..., 10987654321-12345678910, 1110987654321-1234567891011, etc.

Order of the Mongean shuffle permutation of 2n cards: a(n) is least number m for which either 2^m + 1 or 2^m - 1 is divisible by 4n + 1.

a(n) = smallest k >= 1 such that {1^n, 2^n, 3^n, ..., k^n} can be partitioned into two sets with equal sum.

Number of bar segments in a certain way of representing the integers graphically.

Zeroth row of infinite Latin square heading to +oo.

Coordination sequence T1 for Zeolite Code SAO.

Coordination sequence T2 for Zeolite Code SAO.

Coordination sequence T3 for Zeolite Code SAO.

Coordination sequence T4 for Zeolite Code SAO.

Place n distinguishable balls in n boxes (in n^n ways); let T(n,k) = number of ways that the maximum in any box is k, for 1 <= k <= n; sequence gives triangle of numbers T(n,k).

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives triangle of numbers f(n,k)/n.

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives f(n,2)/n.

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives f(n,3)/n.

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1 <= k <= n; sequence gives f(n,n-2)/n.

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives f(n,4)/n.

Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives f(n,2).

a(n) = n*(n - 1)^3/2.

a(n) = n*(n-1)^4/2.

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

Zeroth row of infinite Latin square heading to -oo.

Vertical para-Fibonacci sequence: takes value i on later (i.e., b_j, j >= 2) terms of i-th Fibonacci sequence defined by b_0 = i, b_1 = [ tau(i+1) ].

The left budding sequence: number of i such that 0 < i <= n and 0 < {phi*i} <= {phi*n}, where {} denotes the fractional part and phi = A001622.

The right budding sequence: # of i such that 0 < i <= n and {tau*n} <= {tau*i} < 1, where {} is fractional part.

Number of nondecreasing sequences that are differences of two permutations of 1,2,...,n.

Fermat's Last Theorem: a(n) = 1 if x^n + y^n = z^n has a nontrivial solution in integers, otherwise a(n) = 0.

Grundy function of game in which each player has to divide precisely one set of coins into two subsets of different sizes.

From George Gilbert's marks problem: jumping 3 marks at a time (initial positions).

From George Gilbert's marks problem: jumping 3 marks at a time (initial positions).

Conway's "para-budding" sequence.

From George Gilbert's marks problem: jumping 4 marks at a time (initial positions).

From George Gilbert's marks problem: jumping 4 marks at a time (final positions).

Decimal expansion of 2*Pi*e.

Decimal expansion of 2*Pi*e/3.

Decimal expansion of 2*Pi*e/5.

Decimal expansion of 2*Pi*e/7.

Decimal expansion of 2*Pi*e/9.

Decimal expansion of 2*Pi*e/11.

Decimal expansion of 2*Pi*e/13.

Decimal expansion of 2*Pi*e/15.

Decimal expansion of 2*Pi*e/17.

Decimal expansion of 2*Pi*e/19.

Decimal expansion of 2*Pi*e/21.

Decimal expansion of 2*Pi*e/23.

Decimal expansion of Pi*e.

Decimal expansion of Pi*e/2.