A187185 Parse the infinite string 0123456012345601234560... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 01, 23, 45, 60, 12, 34, 56, 012, ...; a(n) = length of n-th phrase.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 15, 14, 15, 14, 15, 14, 15, 14, 15, 14, 15, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18

Offset

1,8

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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Formula

After the initial block of seven 1's, the sequence is quasi-periodic with period 49, increasing by 7 after each block.

From Colin Barker, Jan 31 2020: (Start)

G.f.: x*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42 + x^43 - x^44 + x^45 - x^46 + x^47 - x^48 - x^50 + x^51 - x^52 + x^53 - x^54 + x^55) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42)).

a(n) = a(n-1) + a(n-49) - a(n-50) for n>56.

(End)

Mathematica

Join[{1, 1, 1, 1, 1, 1}, LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8}, 114]] (* Ray Chandler, Aug 26 2015 *)

Prog

(PARI) Vec(x*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42 + x^43 - x^44 + x^45 - x^46 + x^47 - x^48 - x^50 + x^51 - x^52 + x^53 - x^54 + x^55) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 + x^7 + x^14 + x^21 + x^28 + x^35 + x^42)) + O(x^80)) \\ Colin Barker, Jan 31 2020

Crossrefs

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

Sequence in context: A133877 A132270 A195174 * A054896 A052364 A052374

Adjacent sequences: A187182 A187183 A187184 * A187186 A187187 A187188

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 06 2011

Status

approved