Sequences

Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).

Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5) and cn(4,5) <= cn(2,5) and cn(4,5) <= cn(3,5)).

Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).

Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).

Number of partitions satisfying (cn(0,5) = 0 and cn(2,5) = cn(3,5)).

Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).

Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).

Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) = cn(4,5)).

Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).

Number of partitions satisfying (cn(2,5) = cn(3,5) = 0).

Number of partitions satisfying (cn(0,5) = cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

Number of partitions satisfying cn(1,5) = cn(4,5) = 0.

Number of partitions satisfying (cn(2,5) = cn(3,5) = 0 and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

Number of partitions satisfying (cn(0,5) = cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).

Number of partitions satisfying (cn(1,5) = cn(4,5) = 0 and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).

a(n) = A036800(n)/2.

a(n) = 26 + 2^(n+1)*(-13 +9*n -3*n^2 +n^3).

A036827/2.

a(n) = Sum_{k=0..n-1} C(3*k,k)*C(3*n-3*k-2,n-k-1).

Schoenheim bound L_1(n,n-4,n-5).

Schoenheim bound L_1(n,4,3).

Schoenheim bound L_1(n,5,4).

Schoenheim bound L_1(n,6,5).

Schoenheim bound L_1(n,7,6).

Schoenheim bound L_1(n,8,7).

Schoenheim bound L_1(n,9,8).

Schoenheim bound L_1(n,n-5,n-6).

Triangle read by rows: T(n,k) = value of Schoenheim bound L_1(n+2,k+2,k+1) on covering numbers (0 <= k <= n).

RATS(n): Reverse Add Then Sort the digits.

a(n) is the average of the repeating terms of {T(n,k)} rounded to the nearest integer (rounding up if there's a choice), if {T(n,k)} is eventually periodic; = 0 otherwise. Here T(n,k) is the "phi/sigma tug-of-war sequence with seed n" defined by T(n,1) = phi(n), T(n,2) = sigma(phi(n)), T(n,3) = phi(sigma(phi(n))), ..., T(n,k) = phi(T(n,k-1)) if k is odd and = sigma(T(n,k-1)) if k is even.

Smallest number k such that floor[(the number of digits in k!) / k] is greater than any j < k.

Smallest leg in right triangle with relatively prime sides and hypotenuse 5^n.

Floor(X/Y), where X = concatenation of the triangular numbers and Y = concatenation of natural numbers.

Numbers k such that k / sopfr(k) is an integer, where sopfr = sum-of-prime-factors, A001414.

a(n) = min_{k} {T(n,k)} where T(n,k) is the "phi/sigma tug-of-war sequence with seed n" defined by T(n,1) = phi(n), T(n,2) = sigma(phi(n)), T(n,3) = phi(sigma(phi(n))), ..., T(n,k) = phi(T(n,k-1)) if k is odd and = sigma(T(n,k-1)) if k is even.

Number of partitions of n such that cn(0,5) = cn(2,5) <= cn(3,5) = cn(4,5) <= cn(1,5).

Number of partitions of n such that cn(0,5) = cn(2,5) <= cn(3,5) = cn(4,5) < cn(1,5).

Number of partitions of n such that cn(0,5) = cn(2,5) <= cn(1,5) <= cn(3,5) = cn(4,5).

Number of partitions of n such that cn(1,5) <= cn(0,5) = cn(2,5) <= cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(1,5) = cn(2,5) <= cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) <= cn(1,5) < cn(3,5) = cn(4,5).

Number of partitions of n such that cn(1,5) <= cn(0,5) = cn(2,5) < cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(1,5) = cn(2,5) < cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) < cn(3,5) = cn(4,5) <= cn(1,5).

Number of partitions of n such that cn(0,5) = cn(2,5) <= cn(1,5) = cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) < cn(1,5) <= cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) < cn(1,5) = cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) < cn(3,5) = cn(4,5) < cn(1,5).

Number of partitions of n such that cn(1,5) < cn(0,5) = cn(2,5) <= cn(3,5) = cn(4,5).

Number of partitions of n such that cn(0,5) = cn(2,5) < cn(1,5) < cn(3,5) = cn(4,5).