0,1

The column sequences can also be calculated using sequences which map to associated partitions. For example, 4 32 132 392 ... maps to 5+5+5+4 (n=19) and sequence 5 50 245 840 ... maps to 4+4+4+4+3. Many partitions map to the same sequences since the mapping depends only on the "degree" of the partition. In the above two cases, the degrees are 31 and 41 respectively. At n = 20 the relevant degrees are: 21,31,211,311,22,221,42,212,321,24 and 61. The associated partitions can be permuted with the number of ways as indicated: 3 4 12 20 6 30 15 30 60 15 and 7 ways. Adding these values with the 32 and 50 ways from our first two sequences confirms that A110553(2) = 284.

An examination of the relevant ordered gaussian polynomials reveals the following distributions:

5 4

7 120 120 34 3

112 1127 1190 470 96 9

882 6692 7147 3270 910 162 15

therefore the sequence begins

9

284

3004

19078

...

Cf. A109821.

Sequence in context: A119408 A012234 A012141 this_sequence A118893 A078326 A055792

Adjacent sequences: A110550 A110551 A110552 this_sequence A110554 A110555 A110556

nonn

Alford Arnold (Alford1940(AT)aol.com), Jul 29 2005