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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. 4
1, 19, 452, 10948, 266300, 6484372, 157936172, 3847025764, 93707895260, 2282596837492, 55601016789068, 1354367059315396, 32990588541122684, 803607076375862356, 19574804963320797548, 476816346057854861860, 11614615234500986326556, 282916657894827156657460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal with dimension 2.906...

LINKS

Colin Barker, Table of n, a(n) for n = 0..700

Peter Karpov, InvMem, Item 26

Peter Karpov, Illustration of initial terms (n = 1..4)

Index entries for linear recurrences with constant coefficients, signature (32,-195,216).

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

CROSSREFS

Cf. A285391, A285392, A285393, A285394, A285395, A285396, A285397, A285399, A285400, A026597, A007482.

Sequence in context: A114350 A194730 A012506 * A201798 A284197 A081686

Adjacent sequences:  A285395 A285396 A285397 * A285399 A285400 A285401

KEYWORD

nonn,easy,nice

AUTHOR

Peter Karpov, Apr 23 2017

STATUS

approved

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Last modified August 18 04:42 EDT 2017. Contains 290684 sequences.