A164203 Number of binary strings of length n with equal numbers of 00001 and 10000 substrings.

1, 2, 4, 8, 16, 30, 58, 114, 226, 452, 904, 1808, 3616, 7232, 14464, 28928, 57856, 115712, 231424, 462848, 925696, 1851392, 3702784, 7405568, 14811136, 29622272, 59244544, 118489088, 236978176, 473956352, 947912704, 1895825408, 3791650816, 7583301632

Offset

0,2

Links

R. H. Hardin, Table of n, a(n) for n=0..500

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

a(n) = 113*2^(n-7) for n >= 8. - Brad Clardy, Feb 11 2012

G.f.: (2*x^8+2*x^7+2*x^6+2*x^5-1)/(2*x-1). - Alois P. Heinz, Aug 17 2019

Mathematica

CoefficientList[Series[(2x^8+2x^7+2x^6+2x^5-1)/(2x-1), {x, 0, 50}], x] (* or *) LinearRecurrence[{2}, {1, 2, 4, 8, 16, 30, 58, 114, 226}, 50] (* Harvey P. Dale, Apr 23 2022 *)

Prog

(Empirical) (bc) (z is number of 0's) z=4; for(i=0; i<=500; i++) { if(i<=z)a=2^i else if(i<=2*z)a=2*a-2 else a=2*a; a }

Crossrefs

Sequence in context: A164245 A164236 A164259 * A164178 A335542 A027423

Adjacent sequences: A164200 A164201 A164202 * A164204 A164205 A164206

Keyword

nonn,easy

Author

R. H. Hardin, Aug 11 2009

Status

approved