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A285393 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 or 3; a(n) is the number of cells after n iterations. 8
1, 20, 352, 6080, 104704, 1802240, 31019008, 533872640, 9188540416, 158144921600, 2721848492032, 46846013603840, 806271544459264, 13876822236200960, 238835410589974528, 4110620744461844480, 70748315180918112256, 1217656507884193710080, 20957211028999804813312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal sponge with dimension 2.590...

LINKS

Table of n, a(n) for n=0..18.

Peter Karpov, InvMem, Item 26

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

FORMULA

a(0) = 1, a(1) = 20, a(n) = 20*a(n-1) - 48*a(n-2).

G.f.: 1/(1-20*x+48*x^2).

a(n) = ((13 - 5*sqrt(13))*(10 - 2*sqrt(13))^n + (2*(5 + sqrt(13)))^n*(13 + 5*sqrt(13)))/26.

MATHEMATICA

LinearRecurrence[{20, -48}, {1, 20}, 19]

CROSSREFS

Cf. A285394, A285392, A285391.

Sequence in context: A005748 A230236 A093144 * A156455 A089350 A004292

Adjacent sequences:  A285390 A285391 A285392 * A285394 A285395 A285396

KEYWORD

nonn

AUTHOR

Peter Karpov, Apr 19 2017

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.