23811

Appears in sequences

• One-half the number of permutations of length n without rising or falling successions.at n=7A001266
• Triangle read by rows: T(n,k) is one-half the number of permutations of length n with exactly n-k rising or falling successions, for n >= 1, 1 <= k <= n. T(1,1) = 1 by convention.at n=44A010028
• Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) = number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2).at n=28A010030
• Triangle read by rows: T(n,k) = one-half number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1. T(1,0) = 1 by convention.at n=36A086856
• Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=8.at n=37A143451
• Number of zero-sum -n..n arrays of 4 elements with adjacent element differences also in -n..n.at n=22A202254
• Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x-2)^k.at n=38A246797
• a(n) = 2^n*J(n, 1/2) where J(n, x) are the Jacobsthal polynomials as defined in A322942.at n=7A323232
• Numbers that are the sum of six fourth powers in five or more ways.at n=12A345562
• Numbers that are the sum of six fourth powers in exactly five ways.at n=11A345817