A159572 A triangular array related to ordered partitions and having row sums 1,2,5,14,43,144,523,2048,8597... A047970.

1, 1, 1, 1, 3, 1, 1, 6, 5, 2, 1, 10, 14, 12, 6, 1, 15, 30, 39, 39, 20, 1, 21, 55, 95, 138, 142, 71, 1, 28, 91, 195, 364, 548, 551, 270, 1, 36, 140, 357, 804, 1564, 2317, 2278, 1100

Offset: 1

Author

Alford Arnold, Apr 16 2009

Keywords

• nonn
• tabl
• obsc

Comments

The first five diagonals are essentially A000012, A000217, A000330, A086602 and A159571.

From Alford Arnold, Apr 20 2009: (Start)

After the first two diagonals, each additional diagonal is computed using blocks of source partitions (defined in A053445).

The size of each block increases by powers of two; e.g. 22, 33 222, 44 332 333 2222; etc.

Each source partition can be associated with a specific sequence as illustrated in the below example using partition 332: grow the leftmost value to form 432 then append "1" to form 3321. in like manner, generate 532 4321 and 33211 from the previously formed cases. Note that the number of arrangements are 3, 6+12, and 6+24+30 respectively and that we now have three terms of A006011: 3 18 and 60.

Next we note that 6 39 138 364 804 ... A159571 resulted from summing term by term, the sequences associated with partitions 44 332 333 and 2222:

1...5..14...30...55

3..18..60..150..315

1...7..25...65..140

1...9..39..119..294

(End)

Crossrefs

Cf. A047970 (row sums), A000012, A000217, A000330, A086602, A159571.

Cf. A053445. - Alford Arnold, Apr 20 2009

Extensions

Submitted without a definition. - N. J. A. Sloane, Apr 18 2009

More terms from Alford Arnold, Oct 06 2009