A230216 Number of binary strings of length n avoiding "squares" (that is, repeated blocks of the form xx) with |x| = 3.

1, 2, 4, 8, 16, 32, 56, 104, 192, 352, 648, 1192, 2192, 4032, 7416, 13640, 25088, 46144, 84872, 156104, 287120, 528096, 971320, 1786536, 3285952, 6043808, 11116296, 20446056, 37606160, 69168512, 127220728, 233995400, 430384640, 791600768, 1455980808

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 8*A000073(n) for n >= 3.

From Colin Barker, Aug 09 2019: (Start)

G.f.: (1 + x + x^2 + x^3 + 2*x^4 + 4*x^5) / (1 - x - x^2 - x^3).

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

(End)

Example

For n = 6 there are 8 strings omitted, namely 000000, 001001, ..., 111111, so a(6) = 64-8 = 56.

Prog

(PARI) Vec((1 + x + x^2 + x^3 + 2*x^4 + 4*x^5) / (1 - x - x^2 - x^3) + O(x^40)) \\ Colin Barker, Aug 09 2019

Crossrefs

Cf. A000073, A022087, A229614, A230127, A230177.

Sequence in context: A330012 A329824 A229614 * A326081 A245392 A115909

Adjacent sequences: A230213 A230214 A230215 * A230217 A230218 A230219

Keyword

nonn,easy

Author

Nathaniel Johnston, Oct 11 2013

Status

approved