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

0,2

Comments

a(6917) cannot easily be written in decimal.

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

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.

Sequence in context: A036508 A054319 A006061 * A137466 A062689 A057139

Adjacent sequences: A079212 A079213 A079214 * A079216 A079217 A079218

Keyword

base,nonn

Author

Henry Bottomley, Jan 02 2003

Status

approved