A079215 Catalan paths: numbers starting with 1 and ending with 1 where each digit is positive and adjacent digits differ by 1.

1, 121, 12121, 12321, 1212121, 1212321, 1232121, 1232321, 1234321, 121212121, 121212321, 121232121, 121232321, 121234321, 123212121, 123212321, 123232121, 123232321, 123234321, 123432121, 123432321, 123434321, 123454321

Offset: 0

Author

Henry Bottomley, Jan 02 2003

Keywords

• base
• nonn

Comments

a(6917) cannot easily be written in decimal.

Examples

			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.
		

Crossrefs

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.

Formula

a(n) =A079214(n)+(10^(2+floor[log_10(A079214(n))])-1)/9.