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A285400 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 3; a(n) is the number of cells after n iterations. 4
1, 18, 378, 7938, 166698, 3500658, 73513818, 1543790178, 32419593738, 680811468498, 14297040838458, 300237857607618, 6304995009759978, 132404895204959538, 2780502799304150298, 58390558785387156258, 1226201734493130281418, 25750236424355735909778 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cell configuration converges to a fractal with dimension 2.771...

LINKS

Colin Barker, 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 (21).

FORMULA

a(0) = 1, a(1) = 18, a(n) = 21*a(n-1).

G.f.: (1-3*x)/(1-21*x).

a(n) = 2 * 3^(n+1) * 7^(n-1) for n>0. - Colin Barker, Apr 23 2017

MATHEMATICA

{1}~Join~LinearRecurrence[{21}, {18}, 17]

PROG

(PARI) Vec((1-3*x) / (1-21*x) + O(x^20)) \\ Colin Barker, Apr 23 2017

CROSSREFS

Cf. A285391, A285392, A285393, A285394, A285395, A285396, A285397, A285398, A285399, A026597, A007482.

Sequence in context: A259459 A099276 A221348 * A070943 A252888 A159647

Adjacent sequences:  A285397 A285398 A285399 * A285401 A285402 A285403

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.