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URL: https://oeis.org/A164147

⇱ A164147 - OEIS

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A164147
Number of binary strings of length n with equal numbers of 0000 and 0001 substrings.
3
1, 2, 4, 8, 14, 27, 51, 96, 183, 345, 655, 1244, 2363, 4500, 8570, 16347, 31218, 59678, 114236, 218905, 419979, 806693, 1551247, 2986469, 5756025, 11106397, 21453737, 41486062, 80309039, 155625030, 301882458, 586178231, 1139315438, 2216511306
OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3327 (first 501 terms from R. H. Hardin)
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}] == Count[lst, {0, 0, 0, 1}];
par[lst_List] := Partition[lst, 4, 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), A164178 (equal 00000 and 00001).
Sequence in context: A179817 A214255 A065616 * A321402 A210669 A122026
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 11 2009
STATUS
approved