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A285396 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 2; a(n) is the number of cells after n iterations.

%I A285396 #12 Sep 08 2022 08:46:19
%S A285396 1,21,399,7401,136227,2500437,45845895,840237393,15396839067,
%T A285396 282119272221,5169192919455,94712719519353,1735370171447763,
%U A285396 31796203000166949,582583421696631159,10674336158022192609,195579614965832408523,3583490696858688375405
%N A285396 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 2; a(n) is the number of cells after n iterations.
%C A285396 Cell configuration converges to a fractal with dimension 2.647...
%H A285396 G. C. Greubel, <a href="/A285396/b285396.txt">Table of n, a(n) for n = 0..750</a>
%H A285396 Peter Karpov, <a href="http://inversed.ru/InvMem.htm#InvMem_26">InvMem, Item 26</a>
%H A285396 Peter Karpov, <a href="/A285396/a285396.jpg">Illustration of initial terms (n = 1..4)</a>
%H A285396 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (28,-195,324).
%F A285396 a(0) = 1, a(1) = 21, a(2) = 399, a(n) = 28*a(n-1) - 195*a(n-2) + 324*a(n-3).
%F A285396 G.f.: (1-7*x+6*x^2)/(1-28*x+195*x^2-324*x^3).
%t A285396 LinearRecurrence[{28, -195, 324}, {1, 21, 399}, 20]
%o A285396 (Magma) I:=[1,21,399]; [n le 3 select I[n] else 28*Self(n-1) - 195*Self(n-2) + 324*Self(n-3) : n in [1..41]]; // _G. C. Greubel_, Dec 10 2021
%o A285396 (Sage)
%o A285396 def A285396_list(prec):
%o A285396     P.<x> = PowerSeriesRing(ZZ, prec)
%o A285396     return P( (1-7*x+6*x^2)/(1-28*x+195*x^2-324*x^3) ).list()
%o A285396 A285396_list(40) # _G. C. Greubel_, Dec 10 2021
%Y A285396 Cf. A285391, A285392, A285393, A285394, A285395, A285397, A285398, A285399, A285400.
%K A285396 nonn,easy
%O A285396 0,2
%A A285396 _Peter Karpov_, Apr 19 2017