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A164388 Number of binary strings of length n with no substrings equal to 0000 or 0011. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 18:31 EST 2018. Contains 317240 sequences. (Running on oeis4.)