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URL: https://oeis.org/A164146

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A164146
Number of binary strings of length n with equal numbers of 010 and 101 substrings.
8
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, 3423770240, 6742430340
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
MATHEMATICA
CoefficientList[Series[-(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)), {x, 0, 33}], x] (* Stefano Spezia, Jul 31 2025 *)
CROSSREFS
Column k=1 of A303696.
Column k=0 of A307796.
Sequence in context: A107383 A078025 A178901 * A370582 A279245 A090906
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Aug 11 2009
STATUS
approved