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A164142 Number of binary strings of length n with equal numbers of 001 and 011 substrings 1
1, 2, 4, 6, 10, 16, 30, 56, 110, 208, 396, 740, 1402, 2660, 5116, 9860, 19106, 36996, 71788, 139332, 271040, 527936, 1030348, 2013128, 3938218, 7710220, 15108552, 29627244, 58144136, 114187880, 224405644, 441273096, 868220258, 1709129948 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

R. H. Hardin, Table of n, a(n) for n=0..500

Shalosh B. Ekhad and Doron Zeilberger, Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence. [From N. J. A. Sloane, Apr 07 2012]

FORMULA

Conjecture: n*a(n)+2*(1-2n)*a(n-1) +4(n-1)*a(n-2) +2(2n-3)*a(n-3) +12(2-n)*a(n-4) +4(2n-5)*a(n-5)=0. - R. J. Mathar, Nov 28 2011

CROSSREFS

Sequence in context: A067880 A059749 A334213 * A048833 A204656 A070689

Adjacent sequences:  A164139 A164140 A164141 * A164143 A164144 A164145

KEYWORD

nonn

AUTHOR

R. H. Hardin Aug 11 2009

STATUS

approved

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Last modified September 28 22:03 EDT 2020. Contains 337417 sequences. (Running on oeis4.)