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A285400 Start with a single cell at coordinates (0, 0, 0), then iteratively subdivide the grid into 3 X 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0 or 3; a(n) is the number of cells after n iterations.

%I A285400 #13 Dec 10 2021 11:34:15
%S A285400 1,18,378,7938,166698,3500658,73513818,1543790178,32419593738,
%T A285400 680811468498,14297040838458,300237857607618,6304995009759978,
%U A285400 132404895204959538,2780502799304150298,58390558785387156258,1226201734493130281418,25750236424355735909778
%N A285400 Start with a single cell at coordinates (0, 0, 0), then iteratively subdivide the grid into 3 X 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0 or 3; a(n) is the number of cells after n iterations.
%C A285400 Cell configuration converges to a fractal with dimension 2.771...
%H A285400 Colin Barker, <a href="/A285400/b285400.txt">Table of n, a(n) for n = 0..750</a>
%H A285400 Peter Karpov, <a href="http://inversed.ru/InvMem.htm#InvMem_26">InvMem, Item 26</a>
%H A285400 Peter Karpov, <a href="/A285400/a285400.jpg">Illustration of initial terms (n = 1..4) </a>
%H A285400 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (21).
%F A285400 a(0) = 1, a(1) = 18, a(n) = 21*a(n-1).
%F A285400 G.f.: (1-3*x)/(1-21*x).
%F A285400 a(n) = 2 * 3^(n+1) * 7^(n-1) for n>0. - _Colin Barker_, Apr 23 2017
%F A285400 E.g.f.: (1 + 6*exp(21*x))/7. - _G. C. Greubel_, Dec 09 2021
%t A285400 {1}~Join~LinearRecurrence[{21}, {18}, 17]
%o A285400 (PARI) Vec((1-3*x) / (1-21*x) + O(x^20)) \\ _Colin Barker_, Apr 23 2017
%o A285400 (Sage) [1]+[18*21^(n-1) for n in (1..40)] # _G. C. Greubel_, Dec 09 2021
%o A285400 (Magma) [1] cat [18*21^(n-1): n in [1..40]]; // _G. C. Greubel_, Dec 09 2021
%Y A285400 Cf. A007482, A026597, A285391, A285392, A285393, A285394, A285395, A285396, A285397, A285398, A285399.
%K A285400 nonn,easy
%O A285400 0,2
%A A285400 _Peter Karpov_, Apr 23 2017