A164388 Number of binary strings of length n with no substrings equal to 0000 or 0011.

1, 2, 4, 8, 14, 25, 45, 80, 142, 253, 450, 800, 1423, 2531, 4501, 8005, 14237, 25320, 45031, 80087, 142433, 253314, 450514, 801230, 1424971, 2534282, 4507169, 8015908, 14256129, 25354235, 45091990, 80195185, 142625502, 253656548, 451123000, 802313060

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 500 terms from R. H. Hardin)

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

Formula

G.f.: (x+1)*(x^2+1)/(x^5-x^3-x^2-x+1). - R. J. Mathar, Nov 28 2011

a(n) = 2^n for n<4, a(4)=14, a(5)=25, a(6)=45, a(7)=80, a(8)=142, a(n)=a(n-1)+a(n-2)+a(n-3))-a(n-5). - Harvey P. Dale, Feb 15 2013

Mathematica

LinearRecurrence[{1, 1, 1, 0, -1}, {14, 25, 45, 80, 142}, 40] (* Harvey P. Dale, Feb 15 2013 *)

Crossrefs

Sequence in context: A164151 A281810 A199925 * A164389 A164401 A164387

Adjacent sequences: A164385 A164386 A164387 * A164389 A164390 A164391

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 11 2017

Status

approved