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.

1, 18, 378, 7938, 166698, 3500658, 73513818, 1543790178, 32419593738, 680811468498, 14297040838458, 300237857607618, 6304995009759978, 132404895204959538, 2780502799304150298, 58390558785387156258, 1226201734493130281418, 25750236424355735909778

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

E.g.f.: (1 + 6*exp(21*x))/7. - G. C. Greubel, Dec 09 2021

Mathematica

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

Prog

(PARI) Vec((1-3*x) / (1-21*x) + O(x^20)) \\ Colin Barker, Apr 23 2017
(Sage) [1]+[18*21^(n-1) for n in (1..40)] # G. C. Greubel, Dec 09 2021
(Magma) [1] cat [18*21^(n-1): n in [1..40]]; // G. C. Greubel, Dec 09 2021

Crossrefs

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

Sequence in context: A259459 A099276 A221348 * A324431 A070943 A252888

Adjacent sequences: A285397 A285398 A285399 * A285401 A285402 A285403

Keyword

nonn,easy

Author

Peter Karpov, Apr 23 2017

Status

approved