A136407 Valid strings, in lexicographic order, of Balls ("1") and Strikes ("2") in a Baseball at-bat. Numbers that contain only 1's and 2's never exceeding 3 total 2's or 4 total 1's, whichever comes first.

1, 2, 11, 12, 21, 22, 111, 112, 121, 122, 211, 212, 221, 222, 1111, 1112, 1121, 1122, 1211, 1212, 1221, 1222, 2111, 2112, 2121, 2122, 2211, 2212, 11121, 11122, 11211, 11212, 11221, 11222, 12111, 12112, 12121, 12122, 12211, 12212, 21111, 21112

Offset

1,2

Comments

The string can be too short to have either 3 total 2's or 4 total 1's, because the batter can be out in various ways, or on base in various ways (hit by pitched ball, balk) before the at-bat ends with strikout or walk. A proper subset of A007931.

Links

Jonathan Vos Post, Mar 31 2008, Table of n, a(n) for n = 1..63

Example

a(14) = 222 represents a strikeout in 3 consecutive pitches. a(15) = 1111 represents a walk in 4 consecutive pitches.
2221 is the lexicographically earliest element of A007931 not in this sequence, since after 3 strikes the batter is out and there is no 4th pitch in the at-bat.
11111 is the lexicographically earliest element of A007931 without a 2 not in this sequence, since after 4 balls the batter walks and there is no 5th pitch in the at-bat. Technically, this sequence contains the null string (the batter is out without a pitch being thrown, in several ways) but that is not properly represented as a string of 1s and 2s in the OEIS.

Crossrefs

Cf. A007931, A115380, A121379, A121403.

Sequence in context: A089604 A038114 A007931 * A214215 A136999 A271372

Adjacent sequences: A136404 A136405 A136406 * A136408 A136409 A136410

Keyword

base,easy,fini,nonn

Author

Jonathan Vos Post, Mar 31 2008

Status

approved