A164161 Number of binary strings of length n with equal numbers of 0001 and 1000 substrings.

1, 2, 4, 8, 14, 26, 50, 100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, 819200, 1638400, 3276800, 6553600, 13107200, 26214400, 52428800, 104857600, 209715200, 419430400, 838860800, 1677721600, 3355443200, 6710886400, 13421772800

Offset

0,2

Links

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

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]

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

Formula

G.f.: (2*x^6+2*x^5+2*x^4-1)/(2*x-1). - Alois P. Heinz, May 05 2026

Prog

(Empirical) (bc) (z is number of 0's) z=3; 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: A164167 A164169 A164166 * A068011 A384209 A048238

Adjacent sequences: A164158 A164159 A164160 * A164162 A164163 A164164

Keyword

nonn,easy

Author

R. H. Hardin, Aug 11 2009

Status

approved