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URL: https://oeis.org/A285398

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A285398
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.
10
1, 19, 452, 10948, 266300, 6484372, 157936172, 3847025764, 93707895260, 2282596837492, 55601016789068, 1354367059315396, 32990588541122684, 803607076375862356, 19574804963320797548, 476816346057854861860, 11614615234500986326556, 282916657894827156657460
OFFSET
0,2
COMMENTS
Cell configuration converges to a fractal with dimension 2.906...
FORMULA
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).
G.f.: (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3).
MATHEMATICA
{1}~Join~LinearRecurrence[{32, -195, 216}, {19, 452, 10948}, 17]
PROG
(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
(SageMath)
def A285398_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3) ).list()
A285398_list(40) # G. C. Greubel, Dec 09 2021
(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
KEYWORD
nonn,easy,nice
AUTHOR
Peter Karpov, Apr 23 2017
STATUS
approved