A285396 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 2; a(n) is the number of cells after n iterations.

1, 21, 399, 7401, 136227, 2500437, 45845895, 840237393, 15396839067, 282119272221, 5169192919455, 94712719519353, 1735370171447763, 31796203000166949, 582583421696631159, 10674336158022192609, 195579614965832408523, 3583490696858688375405

Offset: 0

Author

Peter Karpov, Apr 19 2017

Keywords

• nonn
• easy

Comments

Cell configuration converges to a fractal with dimension 2.647...

Links

• G. C. Greubel, 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 (28,-195,324).

Crossrefs

Cf. A285391, A285392, A285393, A285394, A285395, A285397, A285398, A285399, A285400.

Programs

Magma

I:=[1,21,399]; [n le 3 select I[n] else 28*Self(n-1) - 195*Self(n-2) + 324*Self(n-3) : n in [1..41]]; // G. C. Greubel, Dec 10 2021

Mathematica

LinearRecurrence[{28, -195, 324}, {1, 21, 399}, 20]

Sage

def A285396_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-7*x+6*x^2)/(1-28*x+195*x^2-324*x^3) ).list()
A285396_list(40) # G. C. Greubel, Dec 10 2021

Formula

a(0) = 1, a(1) = 21, a(2) = 399, a(n) = 28*a(n-1) - 195*a(n-2) + 324*a(n-3).

G.f.: (1-7*x+6*x^2)/(1-28*x+195*x^2-324*x^3).