A164178 Number of binary strings of length n with equal numbers of 00000 and 00001 substrings.

1, 2, 4, 8, 16, 30, 59, 115, 224, 436, 851, 1657, 3231, 6300, 12287, 23966, 46762, 91250, 178107, 347709, 678959, 1326050, 2590430, 5061449, 9891729, 19335866, 37805063, 73931821, 144613480, 282932141, 553671863, 1083726319, 2121700836, 4154763584

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 [math.CO], 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence. [From N. J. A. Sloane, Apr 07 2012]

Mathematica

tup[n_] := Tuples[{0, 1}, n];
cou[lst_List] := Count[lst, {0, 0, 0, 0, 0}] == Count[lst, {0, 0, 0, 0, 1}];
par[lst_List] := Partition[lst, 5, 1];
a[n_] := a[n] = Map[cou, Map[par, tup[n]]] // Boole // Total;
Monitor[Table[a[n], {n, 0, 18}], {n, Table[a[m], {m, 0, n - 1}]}] (* Robert P. P. McKone, Apr 03 2024 *)

Crossrefs

Cf. A163493 (equal 00 and 01), A164137 (equal 000 and 001), A164147 (equal 0000 and 0001).

Sequence in context: A164236 A164259 A164203 * A335542 A027423 A140410

Adjacent sequences: A164175 A164176 A164177 * A164179 A164180 A164181

Keyword

nonn

Author

R. H. Hardin, Aug 11 2009

Status

approved