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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
Peter Karpov, InvMem, Item 26
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
Sequence in context: A005748 A230236 A093144 * A156455 A358365 A089350
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.)