|
%I #15 Mar 08 2021 10:56:14
%S 0,0,0,0,15,75,225,525,1050,1890,3150,4950,7425,10725,15015,20475,
%T 27300,35700,45900,58140,72675,89775,109725,132825,159390,189750,
%U 224250,263250,307125,356265,411075,471975,539400,613800,695640,785400,883575,990675,1107225
%N Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 161280.
%H Colin Barker, <a href="/A266395/b266395.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _Colin Barker_, Dec 29 2015: (Start)
%F a(n) = 5*(n-1)*(n-2)*(n-3)*(n-4)/8 = 15*A000332(n-1).
%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>5.
%F G.f.: 15*x^5 / (1-x)^5.
%F (End)
%o (PARI) concat(vector(4), Vec(15*x^5/(1-x)^5 + O(x^50))) \\ _Colin Barker_, May 05 2016
%Y Number of orbits of Aut(Z^7) as function of the infinity norm A000579, A154286, A102860, A002412, A045943, A115067, A008586, A008585, A005843, A001477, A000217.
%K nonn,easy
%O 1,5
%A _Philippe A.J.G. Chevalier_, Dec 29 2015
|
