A371662 - OEIS

%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