A164428 Number of binary strings of length n with no substrings equal to 0000, 0011, or 1001.

1, 2, 4, 8, 13, 22, 37, 62, 104, 175, 294, 494, 830, 1395, 2344, 3939, 6619, 11123, 18691, 31409, 52780, 88693, 149041, 250452, 420864, 707229, 1188441, 1997081, 3355934, 5639380, 9476526, 15924546, 26759925, 44967917, 75564988, 126980925, 213381292

Offset

0,2

Links

R. H. Hardin and Harvey P. Dale, Table of n, a(n) for n = 0..1000 (terms n=4..500 from R. H. Hardin)

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

Formula

G.f.: -(x+1)*(x^2+1)*(x^4-x^3-1)/(x^5-x^4-x^2-x+1). - R. J. Mathar, Jan 19 2011

Example

From Tom Edgar, Feb 10 2015: (Start)
When n=4, there are 16 binary strings of length 4 and 3 of them are the ones to avoid, so a(4) = 13.
When n=5, there are 32 binary strings of length 5; the ones including a substring of the indicated form are '00000', '10000', '00001', '00011', '10011', '00110', '00111', 01001', '11001', and '10010'. Since there are 10 to avoid, we have a(5) = 22.
(End)

Mathematica

Join[{1, 2, 4}, LinearRecurrence[{1, 1, 0, 1, -1}, {8, 13, 22, 37, 62}, 40]] (* Harvey P. Dale, Feb 10 2015 *)

Crossrefs

Sequence in context: A338761 A023600 A164437 * A164507 A164414 A164411

Adjacent sequences: A164425 A164426 A164427 * A164429 A164430 A164431

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

Offset changed, terms prepended accordingly, and b-file amended by Harvey P. Dale, Feb 11 2015

Status

approved