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A267139 Decimal representation of the n-th iteration of the "Rule 103" elementary cellular automaton starting with a single ON (black) cell. 1
1, 6, 6, 117, 60, 1931, 376, 32535, 752, 523823, 1504, 8387679, 3008, 134215871, 6016, 2147479935, 12032, 34359730943, 24064, 549755799039, 48128, 8796092992511, 96256, 140737488295935, 192512, 2251799813566463, 385024, 36028797018726399, 770048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (0,19,0,-50,0,32).

FORMULA

From Colin Barker, Jan 11 2016: (Start)

a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>10.

G.f.: (1+6*x-13*x^2+3*x^3-4*x^4+8*x^5-496*x^6+1504*x^7-3584*x^8-1536*x^9+4096*x^10) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).

(End)

MATHEMATICA

rule=103; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

PROG

(PARI) Vec((1+6*x-13*x^2+3*x^3-4*x^4+8*x^5-496*x^6+1504*x^7-3584*x^8-1536*x^9+4096*x^10) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)) + O(x^40)) \\ Colin Barker, Jan 11 2016

CROSSREFS

Cf. A267136.

Sequence in context: A146892 A085804 A012125 * A170915 A123190 A244956

Adjacent sequences:  A267136 A267137 A267138 * A267140 A267141 A267142

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 10 2016

STATUS

approved

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Last modified February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)