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A285392 Start with a single cell at coordinates (0, 0), then iteratively subdivide the grid into 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0; a(n) is the number of cells after n iterations. 10
1, 5, 36, 264, 1944, 14328, 105624, 778680, 5740632, 42321528, 312006168, 2300197176, 16957700568, 125016939000, 921660044184, 6794737129656, 50092713636696, 369297577174392, 2722565630929176, 20071519752269880, 147972890199278808, 1090897774766270712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal carpet with dimension 1.818...

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Peter Karpov, InvMem, Item 26

Peter Karpov, Illustration of cell configuration after 5 iterations

Index entries for linear recurrences with constant coefficients, signature (9,-12).

FORMULA

a(0) = 1, a(1) = 5, a(2) = 36, a(n) = 9*a(n-1) - 12*a(n-2).

G.f.: (1-4*x+3*x^2)/(1-9*x+12*x^2).

a(n) = (2^(-3-n)*((9-sqrt(33))^n*(-13+3*sqrt(33)) + (9+sqrt(33))^n*(13+3*sqrt(33)))) / sqrt(33) for n>0. - Colin Barker, Apr 18 2017

MATHEMATICA

{1}~Join~LinearRecurrence[{9, -12}, {5, 36}, 16]

PROG

(PARI) Vec((1 - x)*(1 - 3*x) / (1 - 9*x + 12*x^2) + O(x^30)) \\ Colin Barker, Apr 18 2017

CROSSREFS

Cf. A285391.

Sequence in context: A098305 A055270 A164110 * A201351 A253470 A188899

Adjacent sequences:  A285389 A285390 A285391 * A285393 A285394 A285395

KEYWORD

nonn,easy

AUTHOR

Peter Karpov, Apr 18 2017

EXTENSIONS

More terms from Colin Barker, Apr 18 2017

STATUS

approved

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