# increasing or decreasing subsequence

Henry in Rotherhithe se16 at btinternet.com
Sat Mar 13 22:42:43 CET 2004

```I would have expected the initial sequence to be the same as the partition
numbers http://www.research.att.com/projects/OEIS?Anum=A000041
at least up to a(9)=30 rather than the 51 you have below.

Indeed the only reason the sequences are not always the partition numbers is
that your concatentation is in decimal - a larger base would mean that we
concatenated more single digits.

Regards

Henry Bottomley

-----Original Message-----
From: bouyao
Sent: 13 March 2004 01:06
To: seqfan at ext.jussieu.fr
Subject: increasing or decreasing subsequence

Dear seqfan,

if we denote S(n) concatenation of numbers

How many increasing subsequence we can extract of S(n) ?

Examples S(n) = successive numbers
S(6) = 123456
increasing subsequence are :

1,2,3,4,5,6
1,2,3,4,56
1,2,3,456
1,2,34,56
1,2,3456
1,23,456
1,23456
12,34,56
12,3456
123,456
123456

for n=6 whe have 11 increasing subsequences (a(6)=11)

and our sequence is 1,2,3,5,7,11,15,22,51,...

```

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