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A285399 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 2; a(n) is the number of cells after n iterations. 4
1, 13, 182, 2548, 35672, 499408, 6991712, 97883968, 1370375552, 19185257728, 268593608192, 3760310514688, 52644347205632, 737020860878848, 10318292052303872, 144456088732254208, 2022385242251558912, 28313393391521824768, 396387507481305546752 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal with dimension 2.402...

LINKS

Colin Barker, Table of n, a(n) for n = 0..850

Peter Karpov, InvMem, Item 26

Peter Karpov, Illustration of initial terms (n = 1..4)

Index entries for linear recurrences with constant coefficients, signature (14).

FORMULA

a(0) = 1, a(1) = 13, a(n) = 14*a(n-1).

G.f.: (1-x)/(1-14*x).

a(n) = 13 * 14^(n-1) for n>0. - Colin Barker, Apr 23 2017

MAPLE

A285399:=n->13*14^(n-1): 1, seq(A285399(n), n=1..30); # Wesley Ivan Hurt, Apr 23 2017

MATHEMATICA

{1}~Join~LinearRecurrence[{14}, {13}, 18]

PROG

(PARI) Vec((1-x) / (1-14*x) + O(x^20)) \\ Colin Barker, Apr 23 2017

CROSSREFS

Cf. A285391, A285392, A285393, A285394, A285395, A285396, A285397, A285398, A285400, A026597, A007482.

Sequence in context: A097260 A178303 A158548 * A268413 A274345 A227503

Adjacent sequences:  A285396 A285397 A285398 * A285400 A285401 A285402

KEYWORD

nonn,easy

AUTHOR

Peter Karpov, Apr 23 2017

STATUS

approved

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