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A164141 Number of binary strings of length n with equal numbers of 001 and 010 substrings. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)