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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. 10
 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 G. C. Greubel, Table of n, a(n) for n = 0..750 Peter Karpov, InvMem, Item 26 Peter Karpov, Illustration of initial terms (n = 1..4) Index entries for linear recurrences with constant coefficients, signature (20,-48). 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. a(n) = (4*sqrt(3))^n * ChebyshevU(n, 5/(2*sqrt(3))). - G. C. Greubel, Dec 11 2021 MATHEMATICA LinearRecurrence[{20, -48}, {1, 20}, 19] PROG (Magma) [n le 2 select (20)^(n-1) else 20*Self(n-1) - 48*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 11 2021 (Sage) [(4*sqrt(3))^n * chebyshev_U(n, 5/(2*sqrt(3))) for n in (0..30)] # G. C. Greubel, Dec 11 2021 CROSSREFS Cf. A285391, A285392, A285394, A285395, A285396, A285397, A285398, A285399, A285400. Sequence in context: A005748 A230236 A093144 * A156455 A358365 A089350 Adjacent sequences: A285390 A285391 A285392 * A285394 A285395 A285396 KEYWORD nonn AUTHOR Peter Karpov, Apr 19 2017 STATUS approved

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Last modified July 15 16:08 EDT 2024. Contains 374333 sequences. (Running on oeis4.)