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A262862
Decimal representation of the n-th iteration of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.
3
1, 5, 17, 93, 273, 1501, 4369, 24029, 69905, 384477, 1118481, 6151645, 17895697, 98426333, 286331153, 1574821341, 4581298449, 25197141469, 73300775185, 403154263517, 1172812402961, 6450468216285, 18764998447377, 103207491460573, 300239975158033
OFFSET
0,2
FORMULA
From Colin Barker, Jan 17 2016 and Apr 17 2019: (Start)
a(n) = 17*a(n-2) - 16*a(n-4) for n>3.
G.f.: (1+5*x+8*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
a(n) = floor((16 + 6*(n mod 2))*4^n / 15). - Karl V. Keller, Jr., Apr 14 2021
MATHEMATICA
rule=147; 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([(16 + 6*(n%2))*4**n//15 for n in range(50)]) # Karl V. Keller, Jr., Apr 14 2021
CROSSREFS
Cf. A262808.
Sequence in context: A197875 A203116 A198090 * A367921 A180382 A250717
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved