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Decimal representation of n-th iteration of the one-dimensional cellular automaton defined by Rule 434, based on the 4-celled von Neumann neighborhood starting with a single black cell.
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%I #13 Jul 16 2020 06:05:59

%S 1,11,81,699,5441,43723,349201,2796731,22364481,178965195,1431573521,

%T 11453377723,91624653121,733009857227,5864040961041,46912529804475,

%U 375299632087361,3002400290556619,24019192622879761,192153592724761787,1537228586572923201,12297829520450964171,98382633680004977681

%N Decimal representation of n-th iteration of the one-dimensional cellular automaton defined by Rule 434, based on the 4-celled von Neumann neighborhood starting with a single black cell.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,16,-128,1,-8,-16,128).

%F a(n) = (1428 + 7*(-4)^n + 2278*(-1)^n + (1800 + 360*i)*(-i)^n + (1800 - 360*i)*i^n - 3*4^n + 85*8^n)/510 where i = sqrt(-1).

%F G.f.: (-1 - 3*x + 23*x^2 - 3*x^3 + 40*x^4 + 624*x^5 - 1856*x^6)/(-1 + 8*x + 16*x^2 - 128*x^3 + x^4 - 8*x^5 - 16*x^6 + 128*x^7).

%Y Cf. A118171, A118173 (similar examples from elementary cellular automata).

%K nonn,base,easy

%O 1,2

%A _Pietro Tiaraju Giavarina dos Santos_, Apr 23 2020