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A285391 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 2; a(n) is the number of cells after n iterations. 10
1, 8, 60, 444, 3276, 24156, 178092, 1312956, 9679500, 71360028, 526086252, 3878455932, 28593068364, 210796144092, 1554048476460, 11456882559036, 84463361313804, 622687661115804, 4590628614276588, 33843405595099644, 249503106984577740, 1839407095720003932 (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) = 8, a(n) = 9*a(n-1) - 12*a(n-2).

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

a(n) = (2^(-1-n)*((9-sqrt(33))^n*(-7+sqrt(33)) + (7+sqrt(33))*(9+sqrt(33))^n)) / sqrt(33). - Colin Barker, Apr 18 2017

MATHEMATICA

LinearRecurrence[{9, -12}, {1, 8}, 16]

PROG

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

CROSSREFS

Cf. A285392.

Sequence in context: A093132 A094169 A129325 * A001267 A099156 A245391

Adjacent sequences:  A285388 A285389 A285390 * A285392 A285393 A285394

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 August 18 04:42 EDT 2017. Contains 290684 sequences.