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.

1, 11, 81, 699, 5441, 43723, 349265, 2797243, 22368577, 178961099, 1431651409, 11453263547, 91625951553, 733007821515, 5864061944913, 46912496398011, 375299968667969, 3002399752698571, 24019198011524177, 192153584105615035, 1537228672804655425, 12297829382490929867

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (8,4,-32,1,-8,-4,32).

Formula

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).

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

Mathematica

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}]

Prog

(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

Crossrefs

Cf. A334340.

Sequence in context: A199557 A003730 A334340 * A111334 A085879 A239459

Adjacent sequences: A335329 A335330 A335331 * A335333 A335334 A335335

Keyword

nonn,easy

Author

Pietro Tiaraju Giavarina dos Santos, Jun 01 2020

Status

approved