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A285395
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 1; a(n) is the number of cells after n iterations.
12
1, 15, 249, 4371, 78693, 1431735, 26159649, 478778379, 8768545197, 160633207887, 2942987702217, 53921188767939, 987955842925365, 18101659807680423, 331665550405417905, 6076909441961837115, 111343619823563404797, 2040083652208572498111, 37379255055440801236953
OFFSET
0,2
COMMENTS
Cell configuration converges to a fractal with dimension 2.647...
FORMULA
a(0) = 1, a(1) = 15, a(2) = 249, a(n) = 28*a(n-1) - 195*a(n-2) + 324*a(n-3).
G.f.: (1-13*x+24*x^2)/(1-28*x+195*x^2-324*x^3).
MATHEMATICA
LinearRecurrence[{28, -195, 324}, {1, 15, 249}, 20]
PROG
(Magma) I:=[1, 15, 249]; [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
(Sage)
def A285395_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-13*x+24*x^2)/(1-28*x+195*x^2-324*x^3) ).list()
A285395_list(40) # G. C. Greubel, Dec 10 2021
KEYWORD
nonn,easy
AUTHOR
Peter Karpov, Apr 19 2017
STATUS
approved