

A164428


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


1



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
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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^4x^31)/(x^5x^4x^2x+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 bfile amended by Harvey P. Dale, Feb 11 2015


STATUS

approved



