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
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).
Crossrefs
Programs
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Magma
[1] cat [18*21^(n-1): n in [1..40]]; // G. C. Greubel, Dec 09 2021
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Mathematica
{1}~Join~LinearRecurrence[{21}, {18}, 17] -
PARI
Vec((1-3*x) / (1-21*x) + O(x^20)) \\ Colin Barker, Apr 23 2017
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Sage
[1]+[18*21^(n-1) for n in (1..40)] # G. C. Greubel, Dec 09 2021
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
Comments