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.

1, 13, 182, 2548, 35672, 499408, 6991712, 97883968, 1370375552, 19185257728, 268593608192, 3760310514688, 52644347205632, 737020860878848, 10318292052303872, 144456088732254208, 2022385242251558912, 28313393391521824768, 396387507481305546752

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

E.g.f.: (1 + 13*exp(14*x))/14. - G. C. Greubel, Dec 09 2021

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
(Sage) [1]+[13*14^(n-1) for n in (1..40)] # G. C. Greubel, Dec 09 2021
(Magma) [1] cat [13*14^(n-1): n in [1..40]]; // G. C. Greubel, Dec 09 2021

Crossrefs

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

Sequence in context: A097260 A178303 A158548 * A297581 A268413 A274345

Adjacent sequences: A285396 A285397 A285398 * A285400 A285401 A285402

Keyword

nonn,easy

Author

Peter Karpov, Apr 23 2017

Status

approved