The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #3 Mar 30 2012 18:51:39
%S 1,121,12121,12321,1212121,1212321,1232121,1232321,1234321,121212121,
%T 121212321,121232121,121232321,121234321,123212121,123212321,
%U 123232121,123232321,123234321,123432121,123432321,123434321,123454321
%N Catalan paths: numbers starting with 1 and ending with 1 where each digit is positive and adjacent digits differ by 1.
%C a(6917) cannot easily be written in decimal.
%F a(n) =A079214(n)+(10^(2+floor[log_10(A079214(n))])-1)/9.
%e Can be constructed from A063171 by starting from a leading 1 and adding 1 to previous digit of a(n) if next digit of A063171 is 1 and subtracting 1 if next digit is 0: e.g. A063171(3)=1100, so digits of a(3) are 1, 1+1=2, 2+1=3, 3-1=2 and 2-1=1 giving a(3)=12321.
%Y Cf. A063171, A079214. a(n) has A000108(m) values with 2m+1 digits. Among the values with 2m+1 digits, the digit k appears a total of A039598(m, k-1) times.
%K base,nonn
%O 0,2
%A _Henry Bottomley_, Jan 02 2003