A288133 - OEIS

A288133

Positions of 0 in A288132; complement of A288134.

1, 2, 4, 7, 12, 21, 38, 71, 136, 265, 522, 1035, 2060, 4109, 8206, 16399, 32784, 65553, 131090, 262163, 524308, 1048597, 2097174, 4194327, 8388632, 16777241, 33554458, 67108891, 134217756, 268435485

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OFFSET

1,2

COMMENTS

a(n+1)/a(n) -> 2. It appears that a(n) = A005126(n-2) for n >= 2.

This conjecture by Kimberling is proved in A288132. - Michel Dekking, Feb 18 2021

LINKS

Table of n, a(n) for n=1..30.

FORMULA

Conjectures from Colin Barker, Jun 09 2017: (Start)

G.f.: x*(1 - 2*x + x^2 - x^3) / ((1 - x)^2*(1 - 2*x)).

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>4.

(End)

Colin Barker's conjectures are a consequence of

a(n) = 2^{n-2} + n - 1 = A005126(n-2) for n >= 2. - Michel Dekking, Feb 18 2021

MATHEMATICA

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "1" -> "11"}]

Table[w[n], {n, 0, 8}]

st = ToCharacterCode[w[11]] - 48 (* A288132 *)

Flatten[Position[st, 0]] (* A288133 *)

Flatten[Position[st, 1]] (* A288134 *)

CROSSREFS

Cf. A288132, A288134.

Sequence in context: A054161 A023433 A190168 * A005126 A054151 A018176

Adjacent sequences: A288130 A288131 A288132 * A288134 A288135 A288136

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 07 2017

STATUS

approved