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A266436
Decimal representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
3
1, 7, 0, 127, 0, 2047, 0, 32767, 0, 524287, 0, 8388607, 0, 134217727, 0, 2147483647, 0, 34359738367, 0, 549755813887, 0, 8796093022207, 0, 140737488355327, 0, 2251799813685247, 0, 36028797018963967, 0, 576460752303423487, 0, 9223372036854775807, 0
OFFSET
0,2
COMMENTS
With the exception of a(1) the same as A266380, A266324 and A266218. - R. J. Mathar, Jan 10 2016
FORMULA
From Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)
a(n) = ((-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.
a(n) = 17*a(n-2)-16*a(n-4) for n>4.
G.f.: (1+7*x-17*x^2+8*x^3+16*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
a(n) = (2*4^n-1)*(n mod 2) + 0^n. - Karl V. Keller, Jr., Jul 06 2021
MATHEMATICA
rule=23; 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
(Python) print([(2*4**n-1)*(n%2) + 0**n for n in range(33)]) # Karl V. Keller, Jr., Jul 06 2021
CROSSREFS
Cf. A241955, A266434, A266435 (binary).
Sequence in context: A352078 A046273 A167317 * A240822 A240810 A024094
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 29 2015
STATUS
approved