

A136407


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


2



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
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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 atbat 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 atbat.
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 atbat. 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 OEIS.


CROSSREFS

Cf. A007931, A115380, A121379, A121403.
Sequence in context: A089604 A038114 A007931 * A214215 A136999 A053880
Adjacent sequences: A136404 A136405 A136406 * A136408 A136409 A136410


KEYWORD

base,easy,fini,nonn


AUTHOR

Jonathan Vos Post, Mar 31 2008


STATUS

approved



