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 A285394 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 or 1; a(n) is the number of cells after n iterations. 8
 1, 7, 116, 1984, 34112, 587008, 10102784, 173879296, 2992652288, 51506839552, 886489481216, 15257461325824, 262597731418112, 4519596484722688, 77787238586384384, 1338804140460998656, 23042295357073522688, 396583308399342518272, 6825635990847321276416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Cell configuration converges to a fractal with dimension 2.590... LINKS Peter Karpov, InvMem, Item 26 Peter Karpov, Illustration of initial terms (n = 1..4) FORMULA a(0) = 1, a(1) = 7, a(2) = 116, a(n) = 20*a(n-1) - 48*a(n-2). G.f.: (1-13*x+24*x^2)/(1-20*x+48*x^2). a(n) = (3*(10-2*sqrt(13))^n*(13+sqrt(13))+(2*(5+sqrt(13)))^n*(91+23*sqrt(13)))/(52*(5+sqrt(13))) for n > 0. MATHEMATICA {1}~Join~LinearRecurrence[{20, -48}, {7, 116}, 18] CoefficientList[Series[(1 - 13x + 24x^2)/(1 - 20x + 48x^2), {x, 0, 40}], x] (* Indranil Ghosh, Apr 19 2017 *) CROSSREFS Cf. A285393, A285392, A285391. Sequence in context: A063399 A220181 A178297 * A251585 A180203 A070067 Adjacent sequences:  A285391 A285392 A285393 * A285395 A285396 A285397 KEYWORD nonn AUTHOR Peter Karpov, Apr 19 2017 STATUS approved

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