This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164146 #32 Jul 31 2025 15:08:34
%S A164146 1,2,4,6,12,20,38,66,124,224,424,788,1502,2838,5438,10386,20004,38508,
%T A164146 74516,144264,280216,544736,1061292,2069596,4042254,7902294,15466842,
%U A164146 30297422,59404174,116558270,228876426,449713994,884199348,1739434972,3423770240,6742430340
%N A164146 Number of binary strings of length n with equal numbers of 010 and 101 substrings.
%H A164146 Alois P. Heinz, <a href="/A164146/b164146.txt">Table of n, a(n) for n = 0..1000</a> (first 501 terms from R. H. Hardin)
%H A164146 Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, 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]
%F A164146 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
%e A164146 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
%t A164146 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 *)
%Y A164146 Cf. A118430, A255386, A260505, A260668, A260697, A303430.
%Y A164146 Column k=1 of A303696.
%Y A164146 Column k=0 of A307796.
%K A164146 nonn,easy
%O A164146 0,2
%A A164146 _R. H. Hardin_, Aug 11 2009