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
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).
Crossrefs
Programs
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Magma
[1] cat [13*14^(n-1): n in [1..40]]; // G. C. Greubel, Dec 09 2021
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Maple
A285399:=n->13*14^(n-1): 1,seq(A285399(n), n=1..30); # Wesley Ivan Hurt, Apr 23 2017
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Mathematica
{1}~Join~LinearRecurrence[{14}, {13}, 18] -
PARI
Vec((1-x) / (1-14*x) + O(x^20)) \\ Colin Barker, Apr 23 2017
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Sage
[1]+[13*14^(n-1) for n in (1..40)] # G. C. Greubel, Dec 09 2021
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
Comments