47622

Appears in sequences

• Triangle read by rows: T(n,k) = number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1.at n=36A001100
• Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions.at n=9A002464
• Triangle: Number of asymmetric semigroups of order n with k idempotents.at n=22A058113
• a(n) = [x^n] (1 + x*(1+x)^(n+1) )^n.at n=6A121675
• Numbers n with property that n^2 is a sum of some 120 successive primes.at n=28A166262
• Number of permutations of 1..2*n+7 with no adjacent elements within n in value.at n=1A179965
• Triangle T(n,k) giving the number of permutations of 1..n with no adjacent elements within k in value, for n >= 2, 1 <= k <= floor(n/2).at n=17A322255
• Number T(n,k) of permutations p of [n] such that |p(i+k) - p(i)| <> k for i in [n-k]; triangle T(n,k), n>=0, 0<=k<=n, read by rows.at n=46A333706
• Triangle read by rows: T(n,k) is the number of permutations of k elements from [1..n] without consecutive adjacent values.at n=54A338526
• Triangle read by rows: T(n,k) gives the number of permutations of length n containing exactly k instances of the 1-box pattern; 0 <= k <= n.at n=45A346462
• Triangle read by rows: T(n, k) is the number of permutations of length n, which contain the maximum number of distinct patterns of length k.at n=43A373877
• Triangle read by rows: T(n,k) is the number of ways to place k non-attacking kings in each row and column of an n X n board, 0 <= k <= floor(n/4) + [n=1].at n=16A387098