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A266590
Decimal representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
2
1, 2, 14, 65, 56, 1799, 224, 31775, 896, 520319, 3584, 8372735, 14336, 134154239, 57344, 2147229695, 229376, 34358722559, 917504, 549751750655, 3670016, 8796076769279, 14680064, 140737423343615, 58720256, 2251799553638399, 234881024, 36028795978776575
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 02 2016 and Apr 18 2019: (Start)
a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>7.
G.f.: (1+2*x-7*x^2+23*x^3-154*x^4+602*x^5+160*x^6-672*x^7) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
Conjecture: a(n) = 2*4^n - 31*2^(n-2) - 1 for odd n > 1; a(n) = 7*2^(n-1) for even n > 1. - Karl V. Keller, Jr., Oct 06 2021
MATHEMATICA
rule=37; 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 *)
CROSSREFS
Sequence in context: A222445 A181394 A335630 * A196977 A254197 A222715
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved