A187181 Parse the infinite string 012012012012... into distinct phrases 0, 1, 2, 01, 20, 12, 012, ...; a(n) = length of n-th phrase.

1, 1, 1, 2, 2, 2, 3, 4, 3, 4, 3, 4, 5, 5, 5, 6, 7, 6, 7, 6, 7, 8, 8, 8, 9, 10, 9, 10, 9, 10, 11, 11, 11, 12, 13, 12, 13, 12, 13, 14, 14, 14, 15, 16, 15, 16, 15, 16, 17, 17, 17, 18, 19, 18, 19, 18, 19, 20, 20, 20, 21, 22, 21, 22, 21, 22, 23, 23, 23, 24, 25, 24, 25, 24, 25, 26, 26, 26, 27, 28, 27, 28, 27, 28, 29, 29, 29, 30, 31, 30, 31, 30, 31, 32, 32, 32, 33, 34, 33, 34

Offset

1,4

Comments

See A187180 for details.

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Formula

After the initial block of three 1's, the sequence is quasi-periodic with period 9, increasing by 3 after each block.

From Colin Barker, Nov 05 2015: (Start)

a(n) = a(n-1) + a(n-9) - a(n-10) for n>12.

G.f.: x*(x^11-x^10-x^8+x^7+x^6+x^3+1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)).

(End)

Example

The sequence begins
1   1   1
2   2   2   3   4   3   4   3   4
5   5   5   6   7   6   7   6   7
8   8   8   9  10   9  10   9  10
11  11  11  12  13  12  13  12  13
14  14  14  15  16  15  16  15  16   ...

Mathematica

Join[{1, 1}, LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 2, 3, 4, 3, 4, 3, 4}, 98]] (* Ray Chandler, Aug 26 2015 *)

Prog

(PARI) Vec(x*(x^11-x^10-x^8+x^7+x^6+x^3+1)/((x-1)^2*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015

Crossrefs

See A187180-A187188 for alphabets of size 2 through 10.

Sequence in context: A228074 A152803 A347102 * A211187 A241504 A342247

Adjacent sequences: A187178 A187179 A187180 * A187182 A187183 A187184

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 06 2011

Status

approved