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%I #30 Apr 03 2024 10:06:18
%S 0,0,0,1,2,5,11,26,56,121,255,539,1123,2332,4808,9891,20262,41413,
%T 84411,171760,348857,707593,1433315,2900313,5863023,11842460
%N Number of binary strings of length n with more 000 than 001 substrings.
%F a(n) = 2^n - A164137(n) - A371682(n).
%e a(5) = 5: 00000, 00001, 01000, 10000, 11000.
%e a(6) = 11: 000000, 000001, 000010, 000011, 010000, 011000, 100000, 100001, 101000, 110000, 111000.
%t tup[n_] := Tuples[{0, 1}, n];
%t cou[lst_List] := Count[lst, {0, 0, 0}] > Count[lst, {0, 0, 1}];
%t par[lst_List] := Partition[lst, 3, 1];
%t a[n_] := a[n] = Map[cou, Map[par, tup[n]]] // Boole // Total;
%t Monitor[Table[a[n], {n, 0, 23}], {n, Table[a[m], {m, 0, n - 1}]}]
%Y Cf. A164137 (equal 000 and 001), A371682 (more 001 than 000).
%K nonn,more
%O 0,5
%A _Robert P. P. McKone_, Apr 03 2024
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