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%I #11 Feb 22 2019 02:13:30
%S 1,2,11,12,21,22,111,112,121,122,211,212,221,222,1111,1112,1121,1122,
%T 1211,1212,1221,1222,2111,2112,2121,2122,2211,2212,11121,11122,11211,
%U 11212,11221,11222,12111,12112,12121,12122,12211,12212,21111,21112
%N 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.
%C 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.
%H Jonathan Vos Post, Mar 31 2008, <a href="/A136407/b136407.txt">Table of n, a(n) for n = 1..63</a>
%e a(14) = 222 represents a strikeout in 3 consecutive pitches. a(15) = 1111 represents a walk in 4 consecutive pitches.
%e 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.
%e 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.
%Y Cf. A007931, A115380, A121379, A121403.
%K base,easy,fini,nonn
%O 1,2
%A _Jonathan Vos Post_, Mar 31 2008
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