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A334244
Decimal representation of n-th iteration of the one-dimensional cellular automaton defined by Rule 950, based on the 4-celled von Neumann neighborhood starting with a single black cell.
1
1, 15, 81, 959, 5185, 61391, 331857, 3929023, 21238849, 251457487, 1359286353, 16093279167, 86994326593, 1029969866703, 5567636901969, 65918071468991, 356328761726017, 4218756574015439, 22805040750465105, 270000420736988095, 1459522608029766721, 17280026927167238095
OFFSET
1,2
COMMENTS
a(n) is the decimal representation of the n-th step based on a simple initial condition, when a(1) = 1.
FORMULA
a(n) = (-1040 + 130*(-1)^n - (504 + 504*i)*(-i)^n - (504 - 504*i)*i^n + 1607*2^(3*n) + 311*(-1)^n*2^(3*n))/8190 where i = sqrt(-1).
G.f.: (1 + 15*x + 17*x^2 - x^3)/(1 - 64*x^2 - x^4 + 64*x^6).
From G. C. Greubel, May 29 2020: (Start)
a(n) = ( (1607 + 311*(-1)^n)*8^n - (1040 - 130*(-1)^n) - 1008*sqrt(2)*cos((2*n-1)*Pi/4) )/8190.
E.g.f.: (959*cosh(8*x) + 648*sinh(8*x) - 455*cosh(x) - 585*sinh(x) - 504*(cos(x) + sin(x)) )/4095.
(End)
a(n) = 64*a(n-2) + a(n-4) - 64*a(n-6) for n>6. - Colin Barker, Jun 10 2020
MATHEMATICA
Table[((1607 +311*(-1)^n)*8^n -1040 +130*(-1)^n -1008*Sqrt[2]*Cos[(2*n-1)*Pi/4] )/8190, {n, 25}] (* G. C. Greubel, May 29 2020 *)
PROG
(PARI) Vec(x*(1 + 15*x + 17*x^2 - x^3) / ((1 - x)*(1 + x)*(1 - 8*x)*(1 + 8*x)*(1 + x^2)) + O(x^20)) \\ Colin Barker, Jun 10 2020
CROSSREFS
Cf. A118171, A118173 (similar examples from elementary cellular automata).
Sequence in context: A213552 A060581 A253222 * A284900 A065103 A279395
KEYWORD
nonn
STATUS
approved