cp's OEIS Frontend

A335332 Decimal representation of n-th iteration of the one-dimensional cellular automaton defined by Rule 954, based on the 4-celled von Neumann neighborhood starting with a single black cell.

%I A335332 #10 Jul 12 2020 18:03:38
%S A335332 1,11,81,699,5441,43723,349265,2797243,22368577,178961099,1431651409,
%T A335332 11453263547,91625951553,733007821515,5864061944913,46912496398011,
%U A335332 375299968667969,3002399752698571,24019198011524177,192153584105615035,1537228672804655425,12297829382490929867
%N A335332 Decimal representation of n-th iteration of the one-dimensional cellular automaton defined by Rule 954, based on the 4-celled von Neumann neighborhood starting with a single black cell.
%H A335332 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,4,-32,1,-8,-4,32).
%F A335332 G.f.: (-1 - 3*x + 11*x^2 - 39*x^3 + 124*x^4 + 12*x^5 - 96*x^6 - 2304*x^7 + 7168*x^8)/(-1 + 8*x + 4*x^2 - 32*x^3 + x^4 - 8*x^5 - 4*x^6 + 32*x^7).
%F A335332 a(n) = 8*a(n-1) + 4*a(n-2) - 32*a(n-3) + a(n-4) - 8*a(n-5) - 4*a(n-6) + 32*a(n-7) for n>9. - _Colin Barker_, Jun 11 2020
%t A335332 Table[DifferenceRoot[Function[{y, n}, {4872 + 32 y[n] + 28 y[1 + n] + 20 y[2 + n] + 21 y[3 + n] - 11 y[4 + n] - 7 y[5 + n] + y[6 + n] == 0, y[1] == 1, y[2] == 11, y[3] == 81, y[4] == 699, y[5] == 5441, y[6] == 43723, y[7] == 349265, y[8] == 2797243}]][n], {n, 1, 30}]
%o A335332 (PARI) Vec(x*(1 + 3*x - 11*x^2 + 39*x^3 - 124*x^4 - 12*x^5 + 96*x^6 + 2304*x^7 - 7168*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 8*x)*(1 + x^2)) + O(x^40)) \\ _Colin Barker_, Jun 11 2020
%Y A335332 Cf. A334340.
%K A335332 nonn,easy
%O A335332 1,2
%A A335332 _Pietro Tiaraju Giavarina dos Santos_, Jun 01 2020