A371662 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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