A164141 Number of binary strings of length n with equal numbers of 001 and 010 substrings.

1, 2, 4, 6, 10, 19, 33, 58, 110, 205, 379, 723, 1383, 2630, 5056, 9770, 18846, 36485, 70891, 137785, 268197, 523176, 1021490, 1996255, 3906299, 7650804, 14995686, 29417270, 57751714, 113448331, 223002449, 438614490, 863149766, 1699458781

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]

Formula

Conjecture: (n+1)*a(n) +(-4*n-1)*a(n-1) +(8*n-9)*a(n-2) +(-14*n+27)*a(n-3) +(19*n-40)*a(n-4) +2*(-11*n+35)*a(n-5) +4*(5*n-22)*a(n-6) +8*(-n+5)*a(n-7)=0. - R. J. Mathar, Dec 10 2013

Crossrefs

Sequence in context: A349592 A026680 A317639 * A034872 A032362 A282251

Adjacent sequences: A164138 A164139 A164140 * A164142 A164143 A164144

Keyword

nonn

Author

R. H. Hardin, Aug 11 2009

Status

approved