A371662 Number of binary strings of length n with more 000 than 001 substrings.

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

Links

Table of n, a(n) for n=0..25.

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

Adjacent sequences: A371659 A371660 A371661 * A371663 A371664 A371665

Keyword

nonn,more

Author

Robert P. P. McKone, Apr 03 2024

Status

approved