A334340 - OEIS

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A334340

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.

1, 11, 81, 699, 5441, 43723, 349201, 2796731, 22364481, 178965195, 1431573521, 11453377723, 91624653121, 733009857227, 5864040961041, 46912529804475, 375299632087361, 3002400290556619, 24019192622879761, 192153592724761787, 1537228586572923201, 12297829520450964171, 98382633680004977681

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (8,16,-128,1,-8,-16,128).

FORMULA

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).

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).

CROSSREFS

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

Sequence in context: A181989 A199557 A003730 * A335332 A111334 A085879

Adjacent sequences: A334337 A334338 A334339 * A334341 A334342 A334343

KEYWORD

nonn,base,easy

AUTHOR

Pietro Tiaraju Giavarina dos Santos, Apr 23 2020

STATUS

approved