0,2

The number of entries <= n gives A000041(n) (the partition numbers). The length of column n is also A000041(n).

Write 0..n as column indices. Under each column write a number for each word of length n+1 of nonisomorphic ballot sequences on 2..(n+1), where the number is n+the number of distinct elements of 2..(n+1). So;

0 1 2 3 4 5

1 2 3 4 5 6

... 4 5 6 7

..... 6 6 7

....... 7 8

....... 8 8

......... 9

......... 10

e.g. for n=5, consider 22222, 22223, 22233, 22234, 22334, 22345, 23456, giving 6,7,7,8,8,9,10.

The sequence reads the columns in turn.

Sequence in context: A110532 A049987 A051898 this_sequence A058222 A064064 A101504

Adjacent sequences: A092029 A092030 A092031 this_sequence A092033 A092034 A092035

hard,nonn,tabf

Jon Perry (perry(AT)globalnet.co.uk), Mar 26 2004