%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