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A371662
Number of binary strings of length n with more 000 than 001 substrings.
2
0, 0, 0, 1, 2, 5, 11, 26, 56, 121, 255, 539, 1123, 2332, 4808, 9891, 20262, 41413, 84411, 171760, 348857, 707593, 1433315, 2900313, 5863023, 11842460
OFFSET
0,5
FORMULA
a(n) = 2^n - A164137(n) - A371682(n).
EXAMPLE
a(5) = 5: 00000, 00001, 01000, 10000, 11000.
a(6) = 11: 000000, 000001, 000010, 000011, 010000, 011000, 100000, 100001, 101000, 110000, 111000.
MATHEMATICA
tup[n_] := Tuples[{0, 1}, n];
cou[lst_List] := Count[lst, {0, 0, 0}] > Count[lst, {0, 0, 1}];
par[lst_List] := Partition[lst, 3, 1];
a[n_] := a[n] = Map[cou, Map[par, tup[n]]] // Boole // Total;
Monitor[Table[a[n], {n, 0, 23}], {n, Table[a[m], {m, 0, n - 1}]}]
CROSSREFS
Cf. A164137 (equal 000 and 001), A371682 (more 001 than 000).
Sequence in context: A104237 A085945 A365322 * A005469 A218575 A159929
KEYWORD
nonn,more
AUTHOR
Robert P. P. McKone, Apr 03 2024
STATUS
approved