|
%I #16 Dec 10 2021 11:33:59
%S 1,19,452,10948,266300,6484372,157936172,3847025764,93707895260,
%T 2282596837492,55601016789068,1354367059315396,32990588541122684,
%U 803607076375862356,19574804963320797548,476816346057854861860,11614615234500986326556,282916657894827156657460
%N 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; a(n) is the number of cells after n iterations.
%C Cell configuration converges to a fractal with dimension 2.906...
%H Colin Barker, <a href="/A285398/b285398.txt">Table of n, a(n) for n = 0..700</a>
%H Peter Karpov, <a href="http://inversed.ru/InvMem.htm#InvMem_26">InvMem, Item 26</a>
%H Peter Karpov, <a href="/A285398/a285398.jpg">Illustration of initial terms (n = 1..4)</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (32,-195,216).
%F a(0) = 1, a(1) = 19, a(2) = 452, a(3) = 10948, a(n) = 28*a(n-1) - 195*a(n-2) + 216*a(n-3).
%F G.f.: (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3).
%t {1}~Join~LinearRecurrence[{32, -195, 216}, {19, 452, 10948}, 17]
%o (PARI) Vec((1 - x)*(1 - 3*x)*(1 - 9*x) / (1 - 32*x + 195*x^2 - 216*x^3) + O(x^20)) \\ _Colin Barker_, Apr 23 2017
%o (Sage)
%o def A285398_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3) ).list()
%o A285398_list(40) # _G. C. Greubel_, Dec 09 2021
%o (Magma) I:=[19, 452, 10948]; [1] cat [n le 3 select I[n] else 32*Self(n-1) - 195*Self(n-2) + 216*Self(n-3) : n in [1..41]]; // _G. C. Greubel_, Dec 09 2021
%Y Cf. A007482, A026597, A285391, A285392, A285393, A285394, A285395, A285396, A285397, A285399, A285400.
%K nonn,easy,nice
%O 0,2
%A _Peter Karpov_, Apr 23 2017
|
