A164142 Number of binary strings of length n with equal numbers of 001 and 011 substrings.

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, 3366154648, 6632709500

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 [math.CO], 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence. - N. J. A. Sloane, Apr 07 2012

Formula

n*a(n) + 2*(1-2*n)*a(n-1) + 4*(n-1)*a(n-2) + 2*(2*n-3)*a(n-3) + 12*(2-n)*a(n-4) + 4*(2*n-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