A285397 - OEIS

%I #14 Dec 10 2021 11:33:51

%S 1,26,646,15818,385822,9401330,229023958,5578844858,135894050926,

%T 3310204057250,80632220390758,1964094376340522,47842741143064894,

%U 1165385872796078546,28387257791866411894,691476036231391881242,16843441238514542846350,410283940250387099210114

%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 3; 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="/A285397/b285397.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 <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) = 26, a(2) = 646, a(n) = 28*a(n-1) - 195*a(n-2) + 216*a(n-3).

%F G.f.: (1-6*x+9*x^2)/(1-32*x+195*x^2-216*x^3).

%t LinearRecurrence[{32, -195, 216}, {1, 26, 646}, 18]

%o (PARI) Vec((1 - 3*x)^2 / (1 - 32*x + 195*x^2 - 216*x^3) + O(x^20)) \\ _Colin Barker_, Apr 23 2017

%o (Sage)

%o def A285397_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( (1-6*x+9*x^2)/(1-32*x+195*x^2-216*x^3) ).list()

%o A285397_list(40) # _G. C. Greubel_, Dec 09 2021

%o (Magma)

%o I:=[1, 26, 646]; [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, A285398, A285399, A285400.

%K nonn,easy

%O 0,2

%A _Peter Karpov_, Apr 23 2017