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A129118
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For each permutation p of {1,2,...,n} define minabsjump(p) = min(|p(i) - i|, 1<=i<=n); a(n) is the sum of minabsjumps of all p.
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0
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0, 1, 2, 10, 48, 295, 2068, 16654, 150382, 1508500, 16631696, 199966907, 2603709640, 36501212971
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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MAPLE
| n:=8; with(combinat); P:=permute(n); ct:= 0; for j to factorial(n) do ct:= ct+min(seq(abs(P[j][i]-i), i=1..n)) end do: ct; # yields a(n) for the specified n - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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PROG
| (C++) #include <iostream> #include <vector> #include <algorithm> using namespace std; inline int mabsj(const vector<int> & s) { const int n = s.size() ; int mi =n ; for(int i=0; i<n; i++) { const int thisdiff = abs(s[i]-i-1) ; if ( thisdiff < mi ) mi=thisdiff ; } return mi ; } int main(int argc, char *argv[]) { for(int n=1 ;; n++) { vector<int> s; for(int i=1; i<=n; i++) s.push_back(i) ; unsigned long long resul=0 ; do { resul += mabsj(s) ; } while( next_permutation(s.begin(), s.end()) ) ; cout << n << " " << resul << endl ; } return 0 ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2007
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CROSSREFS
| Cf. A130153, A018927.
Sequence in context: A036918 A200540 A166922 * A037256 A052576 A143147
Adjacent sequences: A129115 A129116 A129117 * A129119 A129120 A129121
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KEYWORD
| more,nonn
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AUTHOR
| Emeric Deutsch, Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 07 2007
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EXTENSIONS
| One more term from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
a(11)-a(13) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2007
a(14) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 24 2010
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