A164146 Number of binary strings of length n with equal numbers of 010 and 101 substrings.

1, 2, 4, 6, 12, 20, 38, 66, 124, 224, 424, 788, 1502, 2838, 5438, 10386, 20004, 38508, 74516, 144264, 280216, 544736, 1061292, 2069596, 4042254, 7902294, 15466842, 30297422, 59404174, 116558270, 228876426, 449713994, 884199348, 1739434972

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 501 terms from R. H. Hardin)

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

G.f.: -(4*x^4-2*x^3-2*x^2+x+sqrt((2*x-1)*(2*x^2-1)*(2*x^2-2*x+1))) / ((x-1)*(2*x-1)*(2*x^2-1)). - Alois P. Heinz, Apr 16 2015

Example

a(5) = 20: 00000, 00001, 00011, 00101, 00110, 00111, 01011, 01100, 01110, 01111, 10000, 10001, 10011, 10100, 11000, 11001, 11010, 11100, 11110, 11111. - Alois P. Heinz, Apr 16 2015

Crossrefs

Cf. A118430, A255386, A260505, A260668, A260697, A303430.

Column k=1 of A303696.

Column k=0 of A307796.

Sequence in context: A107383 A078025 A178901 * A370582 A279245 A090906

Adjacent sequences: A164143 A164144 A164145 * A164147 A164148 A164149

Keyword

nonn,easy

Author

R. H. Hardin, Aug 11 2009

Status

approved