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%I #20 Oct 06 2016 11:52:45
%S 0,0,2,5,9,15,22,32,43,57,72,91,110,134,158,187,216,251,285,326,366,
%T 413,459,513,565,626,685,753,819,895,968,1052,1133,1225,1314,1415,
%U 1512,1622,1728,1847,1962,2091,2215,2354,2488,2637,2781,2941,3095,3266,3431
%N Number of non-Abelian metacyclic groups of order 2^n.
%H Colin Barker, <a href="/A007982/b007982.txt">Table of n, a(n) for n = 1..1000</a>
%H Steven Liedahl, <a href="http://dx.doi.org/10.1006/jabr.1996.0381">Enumeration of metacyclic p-groups</a>, J. Algebra 186 (1996), no. 2, 436-446.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,2,1,-1).
%F a(n) = A136184(n) - floor(n/2) - 1. - _Eric M. Schmidt_, Jan 08 2015
%F G.f.: -x^3*(x^8+x^7-x^6-x^5+2*x^4+2*x^3-3*x-2) / ((x-1)^4*(x+1)^2*(x^2+x+1)). - _Colin Barker_, Jan 12 2015
%t LinearRecurrence[{1,2,-1,-2,-1,2,1,-1},{0,0,2,5,9,15,22,32,43,57,72},60] (* _Harvey P. Dale_, Oct 06 2016 *)
%o (PARI) concat([0,0], Vec(-x^3*(x^8+x^7-x^6-x^5+2*x^4+2*x^3-3*x-2) / ((x-1)^4*(x+1)^2*(x^2+x+1)) + O(x^100))) \\ _Colin Barker_, Jan 12 2015
%K nonn,easy
%O 1,3
%A S. Liedahl
%E a(2) corrected and sequence extended (using A136184) by _Eric M. Schmidt_, Jan 08 2015
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