A143960 a(n) = the n-th positive integer with exactly n zeros and n ones in its binary representation.

2, 10, 38, 142, 542, 2110, 8318, 33022, 131582, 525310, 2099198, 8392702, 33562622, 134234110, 536903678, 2147549182, 8590065662, 34360000510, 137439477758, 549756862462, 2199025352702, 8796097216510, 35184380477438, 140737505132542, 562949986975742

Offset: 1

Author

Leroy Quet, Sep 05 2008

Keywords

• base
• nonn

Examples

			The first of the (10) positive integers with exactly three 0's and three 1's in their binary representation are 35 (100011 in binary), 37 (100101 in binary), 38 (100110 in binary), etc. a(3) is the third of these, which is 38.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A099393.

Programs

Mathematica

Table[FromDigits[Select[Sort[Permutations[Flatten[Table[{1,0},n]]]],#[[1]] == 1&][[n]],2],{n,25}] (* or *) Table[2^(2n-1)+2^n-2,{n,25}] (* or *) LinearRecurrence[{7,-14,8},{2,10,38},25] (* The second and third programs are much faster than the first. *) (* Harvey P. Dale, Mar 11 2022 *)

Formula

a(n) = 2^(2n-1) + 2^n - 2.

G.f.: 2*x*(1-2*x-2*x^2)/((1-x)*(1-4*x)*(1-2*x)). a(n) = 2*A099393(n-1). [R. J. Mathar, Nov 03 2008; G.f. corrected by Georg Fischer, May 12 2019]

Extensions

More terms from R. J. Mathar, Nov 03 2008