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Number of nonsplit type 2 metacyclic 2-groups of order 2^n.
1

%I #16 Jun 13 2015 00:48:22

%S 0,0,0,0,0,0,0,1,2,4,6,10,13,19,24,32,39,50,59,73,85,102,117,138,156,

%T 181,203,232,258,292,322,361,396,440,480,530,575,631,682,744,801,870,

%U 933,1009,1079,1162,1239,1330,1414,1513,1605,1712,1812,1928,2036,2161

%N Number of nonsplit type 2 metacyclic 2-groups of order 2^n.

%C See Theorem 5 of Liedahl. - _Eric M. Schmidt_, Jan 09 2015

%H Colin Barker, <a href="/A007981/b007981.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 G.f.: -x^8*(x^3-x-1) / ((x-1)^4*(x+1)^2*(x^2+x+1)). - _Colin Barker_, Jan 12 2015

%o (PARI) concat([0,0,0,0,0,0,0], Vec(-x^8*(x^3-x-1)/((x-1)^4*(x+1)^2*(x^2+x+1)) + O(x^100))) \\ _Colin Barker_, Jan 12 2015

%K nonn,easy

%O 1,9

%A S. Liedahl

%E More terms and initial zeros from _Eric M. Schmidt_, Jan 11 2015