OFFSET
0,2
COMMENTS
Cell configuration converges to a fractal with dimension 2.906...
LINKS
Colin Barker, Table of n, a(n) for n = 0..700
Peter Karpov, InvMem, Item 26
Peter Karpov, Illustration of initial terms (n = 1..4)
Index entries for linear recurrences with constant coefficients, signature (32,-195,216).
FORMULA
a(0) = 1, a(1) = 19, a(2) = 452, a(3) = 10948, a(n) = 28*a(n-1) - 195*a(n-2) + 216*a(n-3).
G.f.: (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3).
MATHEMATICA
{1}~Join~LinearRecurrence[{32, -195, 216}, {19, 452, 10948}, 17]
PROG
(PARI) Vec((1 - x)*(1 - 3*x)*(1 - 9*x) / (1 - 32*x + 195*x^2 - 216*x^3) + O(x^20)) \\ Colin Barker, Apr 23 2017
(Sage)
def A285398_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-13*x+39*x^2-27*x^3)/(1-32*x+195*x^2-216*x^3) ).list()
A285398_list(40) # G. C. Greubel, Dec 09 2021
(Magma) I:=[19, 452, 10948]; [1] cat [n le 3 select I[n] else 32*Self(n-1) - 195*Self(n-2) + 216*Self(n-3) : n in [1..41]]; // G. C. Greubel, Dec 09 2021
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Peter Karpov, Apr 23 2017
STATUS
approved