0,6

a(n) is also the number of binary sequences of length n-1 in which the longest run of consecutive 0's is exactly three. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Nov 06 2008]

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 155.

J. L. Yucas, Counting special sets of binary Lyndon words, Ars Combin., 31 (1991), 21-29.

T. D. Noe, Table of n, a(n) for n=0..200

Nick Hobson, Python program for this sequence

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

a(n)=2*a(n-1)+a(n-2)-2*a(n-4)-3*a(n-5)-2*a(n-6)-a(n-7). Convolution of Tribonacci and Tetranacci numbers (A000073 and A000078). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006

For example, a(6)=5 counts 1+1+4, 2+4, 4+2, 4+1+1, 1+4+1. - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004

a(6)=5 because there are 5 binary sequences of length 5 in which the longest run of consecutive 0's is exactly 3; 00010,00011,01000,10001,11000 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Nov 06 2008]

a:= n-> (Matrix(7, (i, j)-> if i+1=j then 1 elif j=1 then [2, 1, 0, -2, -3, -2, -1][i] else 0 fi)^n)[1, 5]: seq (a(n), n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 07 2008]

Adjacent sequences: A000099 A000100 A000101 this_sequence A000103 A000104 A000105

Sequence in context: A129983 A083378 A116712 this_sequence A086589 A091596 A077863

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 15 2002

Definition improved by David Callan and Frank Adams-Watters.