%I A136407
%S A136407 1,2,11,12,21,22,111,112,121,122,211,212,221,222,1111,1112,1121,1122,
%T A136407 1211,1212,1221,1222,2111,2112,2121,2122,2211,2212,11121,11122,11211,
%U A136407 11212,11221,11222,12111,12112,12121,12122,12211,12212,21111,21112
%N 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.
%C A136407 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 A136407 Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 31 2008, <a href="b136407.txt">
               Table of n, a(n) for n = 1..63</a>
%e A136407 a(14) = 222 represents a strikeout in 3 consecutive pitches. a(15) = 
               1111 represents a walk in 4 consecutive pitches.
%e A136407 2221 is the lexicographically first 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 A136407 11111 is the lexicographically first 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 OEIS.
%Y A136407 Cf. A115380, A121379, A121403.
%Y A136407 Sequence in context: A089604 A038114 A007931 this_sequence A136999 A053880 
               A063112
%Y A136407 Adjacent sequences: A136404 A136405 A136406 this_sequence A136408 A136409 
               A136410
%K A136407 base,easy,fini,nonn
%O A136407 1,2
%A A136407 Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 31 2008