A064482 Triangle read by rows: T(n,k) (n >= 2, 1<=k<=n-1) is the number of permutations p of 1,...,n with max(|p(i)-p(i-1)|, i=2..n) = k.

2, 2, 4, 2, 10, 12, 2, 18, 52, 48, 2, 32, 146, 300, 240, 2, 54, 372, 1204, 1968, 1440, 2, 86, 954, 4082, 10476, 14640, 10080, 2, 134, 2376, 13348, 46012, 97968, 122400, 80640, 2, 206, 5704, 44274, 186202, 536652, 990960, 1139040, 725760, 2, 312, 13278, 145216, 742940, 2655004, 6562128, 10847520, 11692800, 7257600

Offset

2,1

Comments

T(n,n-1) = A052849; sum(T(n,k),k=1..n-1) = A000142.

Links

Alois P. Heinz, Rows n = 2..18, flattened

Example

Triangle T(n,k) begins:
  2;
  2,   4;
  2,  10,   12;
  2,  18,   52,    48;
  2,  32,  146,   300,   240;
  2,  54,  372,  1204,  1968,  1440;
  2,  86,  954,  4082, 10476, 14640,  10080;
  2, 134, 2376, 13348, 46012, 97968, 122400, 80640;

Prog

(C++) #include <iostream> #include <vector> #include <algorithm> using namespace std; inline int k(const vector<int> & s) { const int n = s.size() ; int kmax = 0 ; for(int i=1; i<n; i++) { const int thisdiff = abs(s[i]-s[i-1]) ; if ( thisdiff > kmax) kmax = thisdiff ; } return kmax ; } int main(int argc, char *argv[]) { for(int n=2 ;; n++) { vector<int> s; for(int i=1; i<=n; i++) s.push_back(i) ; vector<unsigned long long> resul(n); do { resul[k(s)]++ ; } while( next_permutation(s.begin(), s.end()) ) ; for(int i=1; i<n; i++) cout << resul[i] << ", " ; cout << endl ; } return 0 ; } - R. J. Mathar, Oct 11 2007

Crossrefs

Cf. A052849, A000142, A129534.

Sequence in context: A111741 A111793 A349754 * A341699 A294072 A329600

Adjacent sequences: A064479 A064480 A064481 * A064483 A064484 A064485

Keyword

nonn,tabl

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 05 2001

Extensions

More terms from Naohiro Nomoto, Dec 04 2001

More terms from R. J. Mathar, Oct 11 2007

Status

approved