This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164178 #16 Apr 28 2024 11:02:55
%S A164178 1,2,4,8,16,30,59,115,224,436,851,1657,3231,6300,12287,23966,46762,
%T A164178 91250,178107,347709,678959,1326050,2590430,5061449,9891729,19335866,
%U A164178 37805063,73931821,144613480,282932141,553671863,1083726319,2121700836,4154763584
%N A164178 Number of binary strings of length n with equal numbers of 00000 and 00001 substrings.
%H A164178 R. H. Hardin, <a href="/A164178/b164178.txt">Table of n, a(n) for n=0..500</a>
%H A164178 Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, 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]
%t A164178 tup[n_] := Tuples[{0, 1}, n];
%t A164178 cou[lst_List] := Count[lst, {0, 0, 0, 0, 0}] == Count[lst, {0, 0, 0, 0, 1}];
%t A164178 par[lst_List] := Partition[lst, 5, 1];
%t A164178 a[n_] := a[n] = Map[cou, Map[par, tup[n]]] // Boole // Total;
%t A164178 Monitor[Table[a[n], {n, 0, 18}], {n, Table[a[m], {m, 0, n - 1}]}] (* _Robert P. P. McKone_, Apr 03 2024 *)
%Y A164178 Cf. A163493 (equal 00 and 01), A164137 (equal 000 and 001), A164147 (equal 0000 and 0001).
%K A164178 nonn
%O A164178 0,2
%A A164178 _R. H. Hardin_, Aug 11 2009