A371682 Number of binary strings of length n with more 001 than 000 substrings.

0, 0, 0, 1, 3, 8, 18, 41, 89, 191, 400, 833, 1717, 3523, 7184, 14604, 29588, 59822, 120695, 243166, 489271, 983530, 1975416, 3965078, 7954340, 15950301, 31972219, 64069007, 128355352, 257093509, 514864480, 1030937876, 2064045150, 4132012413, 8271156673

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3322

Formula

a(n) = 2^n - A164137(n) - A371662(n).

Example

a(5) = 8: 00100, 00101, 00110, 00111, 01001, 10010, 10011, 11001.
a(6) = 18: 001001, 001010, 001011, 001100, 001101, 001110, 001111, 010010, 010011, 011001, 100100, 100101, 100110, 100111, 101001, 110010, 110011, 111001.

Mathematica

tup[n_] := Tuples[{0, 1}, n];
cou[lst_List] := Count[lst, {0, 0, 1}] > Count[lst, {0, 0, 0}];
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), A371662 (more 000 than 001).

Sequence in context: A240135 A066425 A026679 * A191524 A026756 A341583

Adjacent sequences: A371679 A371680 A371681 * A371683 A371684 A371685

Keyword

nonn

Author

Robert P. P. McKone, Apr 03 2024

Extensions

a(26)-a(34) from Alois P. Heinz, Apr 03 2024

Status

approved