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%I M1069 #28 Jun 21 2018 03:05:47
%S 1,2,4,7,13,23,46,88,186,395,880,1989,4644,10934,26210,63319,154377,
%T 378443,933022,2308956,5735371,14286907,35683814,89324137,224057918,
%U 563033978,1417210456,3572641303,9018885121,22796905055,57692673962,146167385344,370710166434
%N States of a dynamic storage system.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A005595/b005595.txt">Table of n, a(n) for n = 0..200</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms</a>
%H M. D. McIlroy, <a href="http://dx.doi.org/10.1093/comjnl/25.3.388">The number of states of a dynamic storage system</a>, Computer J., 25 (No. 3, 1982), 388-392.
%H M. D. McIlroy, <a href="/A005207/a005207.pdf">The number of states of a dynamic storage system</a>, Computer J., 25 (No. 3, 1982), 388-392. (Annotated scanned copy)
%H <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F Also "DIK" (bracelet, indistinct, unlabeled) transform of 2, 1, 1, 1, ...
%F G.f.: ((2 - 2*x + x^3)/((1 - x)*(1 - x - x^2)) + Sum_{d>0} phi(d)*log((1-x^d)/(1-3*x^d+x^(2*d)))/d)/2. - _Andrew Howroyd_, Jun 20 2018
%o (PARI) seq(n)={Vec((2 - 2*x + x^3)/((1 - x)*(1 - x - x^2)) + sum(d=1, n, eulerphi(d)/d*log((1-x^d)/(1-3*x^d+x^(2*d)) + O(x*x^n))))/2} \\ _Andrew Howroyd_, Jun 20 2018
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E Sequence extended by _Christian G. Bower_
%E Terms a(30) and beyond from _Andrew Howroyd_, Jun 20 2018
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