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A285395 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 1; a(n) is the number of cells after n iterations. 9
1, 15, 249, 4371, 78693, 1431735, 26159649, 478778379, 8768545197, 160633207887, 2942987702217, 53921188767939, 987955842925365, 18101659807680423, 331665550405417905, 6076909441961837115, 111343619823563404797, 2040083652208572498111, 37379255055440801236953 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal with dimension 2.647...

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) = 15, a(2) = 249, a(n) = 28*a(n-1) - 195*a(n-2) + 324*a(n-3).

G.f.: (1-13*x+24*x^2)/(1-28*x+195*x^2-324*x^3).

MATHEMATICA

LinearRecurrence[{28, -195, 324}, {1, 15, 249}, 19]

CROSSREFS

Cf. A285396, A285394, A285393, A285392, A285391.

Sequence in context: A273624 A223424 A218806 * A093147 A218192 A066410

Adjacent sequences:  A285392 A285393 A285394 * A285396 A285397 A285398

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.