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
Offset: 0
Keywords
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]
Programs
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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 }