A207377 Triangle read by rows in which row n lists the parts of the last section of the set of partitions of n in nondecreasing order.

1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 8

Offset: 1

Author

Omar E. Pol, Feb 23 2012

Keywords

• nonn
• tabf

Comments

Starting from the first row; it appears that the total numbers of occurrences of k in k successive rows give the sequence A000041. For more information see A182703.

Examples

			Written as a triangle:
1;
1,2;
1,1,3;
1,1,1,2,2,4;
1,1,1,1,1,2,3,5;
1,1,1,1,1,1,1,2,2,2,2,3,3,4,6;
1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,3,4,5,7;
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4,4,5,6,8;
		

Links

• Alois P. Heinz, Rows n = 1..23, flattened

Crossrefs

Triangle similar to A135010. Mirror of A207378. Row n has length A138137(n). Row sums give A138879. Right border is A000027.

Cf. A000041, A006128, A066186, A138121, A182703, A182712-A182714, A194812.