2,1

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E.g.f.: -(6+6*x^2-4*x^3+x^4)/(-3+12*x-18*x^2+12*x^3-3*x^4). recurrence: a(0)=2, a(n)=(1/6)*GAMMA(n+3)*(3*n+5). [From Thomas Wieder (thomas.wieder(AT)t-online.de), May 02 2009]

[1, 2, 3, 4], "ups"=3, "downs"=0;

[1, 2, 4, 3], "ups"=2, "downs"=0;

[1, 3, 2, 4], "ups"=2, "downs"=0;

[1, 3, 4, 2], "ups"=2, "downs"=0;

[1, 4, 2, 3], "ups"=2, "downs"=0;

[1, 4, 3, 2], "ups"=1, "downs"=0;

[2, 1, 3, 4], "ups"=0, "downs"=1;

[2, 1, 4, 3], "ups"=0, "downs"=2;

[2, 3, 1, 4], "ups"=2, "downs"=0;

[2, 3, 4, 1], "ups"=2, "downs"=0;

[2, 4, 1, 3], "ups"=2, "downs"=0;

[2, 4, 3, 1], "ups"=1, "downs"=0;

[3, 1, 2, 4], "ups"=0, "downs"=1;

[3, 1, 4, 2], "ups"=0, "downs"=2;

[3, 2, 1, 4], "ups"=0, "downs"=2;

[3, 2, 4, 1], "ups"=0, "downs"=2;

[3, 4, 1, 2], "ups"=2, "downs"=0;

[3, 4, 2, 1], "ups"=1, "downs"=0;

[4, 1, 2, 3], "ups"=0, "downs"=1;

[4, 1, 3, 2], "ups"=0, "downs"=2;

[4, 2, 1, 3], "ups"=0, "downs"=2;

[4, 2, 3, 1], "ups"=0, "downs"=2;

[4, 3, 1, 2], "ups"=0, "downs"=2;

[4, 3, 2, 1], "ups"=0, "downs"=3.

(C++) #include <stdio.h> #include <iostream> #include <vector> #include <algorithm> using namespace std ; class UDown { public: vector<int> perm; UDown(int n) { for(int c=0; c < n ; c++) perm.push_back(c) ; } int ups ( const vector<int> & perm) const { int sgn = perm[1]-perm[0] ; int u = 0 ; for(int i=1 ; i < perm.size() ; i++) if ( (perm[i]-perm[i-1])*sgn > 0) u++ ; return u ; } long long int cnt() { long long int a = ups(perm) ; while ( next_permutation(perm.begin(), perm.end()) ) a += ups(perm) ; return a ; } } ; int main(int argc, char *argv[]) { for(int n=2; ; n++) { UDown m(n) ; cout << n << " " << m.cnt() << endl ; } return 0 ; } [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 25 2008]

Cf. A028399, A052582, A062119, A097971.

Sequence in context: A121747 A014508 A141147 this_sequence A111537 A051045 A112912

Adjacent sequences: A120925 A120926 A120927 this_sequence A120929 A120930 A120931

nonn

Thomas Wieder (thomas.wieder(AT)t-online.de), Jul 16 2006

4 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 25 2008