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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.
10
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...
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
KEYWORD
nonn,easy
AUTHOR
Peter Karpov, Apr 23 2017
STATUS
approved