A159711 - OEIS

%I #18 Sep 08 2022 08:45:44

%S 0,0,0,0,0,0,96,1904,23040,221184,1858560,14353152,104742912,

%T 734769152,5010432000,33464217600,220066480128,1430279159808,

%U 9212045819904,58914039332864,374665295953920,2371935399837696,14960708435312640,94072038170296320,589975504803594240

%N Number of permutations of 1..n arranged in a circle with exactly 3 local maxima.

%H Alois P. Heinz, <a href="/A159711/b159711.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (32,-444,3504,-17328,55680,-116288,152320,-113664,36864).

%F G.f.: -16*(144*x^4-444*x^3+296*x^2-73*x+6)*x^6 / ((6*x-1)^2 *(4*x-1)^3 *(2*x-1)^4). - _Alois P. Heinz_, Oct 26 2015

%F a(n) = 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2) for n>1. - _Colin Barker_, Oct 26 2015

%t Table[(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2), {n,0,30}] (* _G. C. Greubel_, Jun 01 2018 *)

%o (PARI) a(n) = if(n==1, 0, 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n +6*n^2)) \\ _Colin Barker_, Oct 26 2015

%o (PARI) concat(vector(6), Vec(-16*x^6*(144*x^4-444*x^3+296*x^2-73*x+6)/(

%o (2*x-1)^4*(4*x-1)^3*(6*x-1)^2) + O(x^30))) \\ _Colin Barker_, Oct 26 2015

%o (Magma) [(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2): n in [0..30]]; // _G. C. Greubel_, Jun 01 2018

%Y Column k=3 of A263789.

%K nonn,easy

%O 0,7

%A _R. H. Hardin_, Apr 20 2009

%E a(17)-a(24) from _Alois P. Heinz_, Oct 26 2015