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A078485 Number of irreducible indecomposable permutations of degree n.

%I A078485 #15 Feb 06 2022 06:52:43
%S A078485 0,1,1,1,7,15,31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535,
%T A078485 131071,262143,524287,1048575,2097151,4194303,8388607,16777215,
%U A078485 33554431,67108863,134217727,268435455,536870911,1073741823,2147483647,4294967295,8589934591
%N A078485 Number of irreducible indecomposable permutations of degree n.
%H A078485 Colin Barker, <a href="/A078485/b078485.txt">Table of n, a(n) for n = 0..1000</a>
%H A078485 M. D. Atkinson and T. Stitt, <a href="http://www.cs.otago.ac.nz/staffpriv/mike/Papers/WreathProduct/Wreathpaper.pdf">Restricted permutations and the wreath product</a>, Preprint, 2002.
%H A078485 M. D. Atkinson and T. Stitt, <a href="http://dx.doi.org/10.1016/S0012-365X(02)00443-0">Restricted permutations and the wreath product</a>, Discrete Math., 259 (2002), 19-36.
%H A078485 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A078485 a(n) = 2^(n-1) - 1 for n > 3.
%F A078485 G.f.: x - 2*x^3 + x/(1-2*x) - x/(1-x).
%F A078485 (1, 7, 15, 31, 63, ...) = row sums of triangle A134065. - _Gary W. Adamson_, Oct 06 2007
%F A078485 a(n) = 3*a(n-1) - 2*a(n-2) for n > 2. - _Colin Barker_, May 27 2016
%o A078485 (PARI) concat(0, Vec(x*(1-2*x+6*x^3-4*x^4)/((1-x)*(1-2*x)) + O(x^50))) \\ _Colin Barker_, May 27 2016
%Y A078485 Cf. A134065.
%K A078485 nonn,easy
%O A078485 0,5
%A A078485 _N. J. A. Sloane_, Jan 04 2003