A092080 Triangle read by rows in which row n lists the partition numbers of the first n positive integers.

1, 1, 2, 1, 2, 3, 1, 2, 3, 5, 1, 2, 3, 5, 7, 1, 2, 3, 5, 7, 11, 1, 2, 3, 5, 7, 11, 15, 1, 2, 3, 5, 7, 11, 15, 22, 1, 2, 3, 5, 7, 11, 15, 22, 30, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42

Offset: 1

Author

Wolfdieter Lang, Mar 19 2004

Keywords

• nonn
• tabl
• easy

Comments

Sequence of row lengths of array A092078.

Interpreted as a sequence a(n) = p(m) = A000041(m) (number of partitions of m) with m := n-L, where L is the largest number from A000217 (triangular numbers) which is less than n.

Row sums give A026905. - Omar E. Pol, Apr 23 2012

Examples

			a(17)= p(2)= 2 because 17 = (15=A000217(5)) + 2.
a(10)= p(4)= 5 because 10 = (6=A000217(3)) + 4 (note that T < n, not <=n, is asked for).
Contribution from _Omar E. Pol_, Apr 24 2012 (Start):
Triangle begins:
1;
1, 2;
1, 2, 3;
1, 2, 3, 5;
1, 2, 3, 5, 7;
1, 2, 3, 5, 7, 11;
1, 2, 3, 5, 7, 11, 15;
1, 2, 3, 5, 7, 11, 15, 22;
1, 2, 3, 5, 7, 11, 15, 22, 30;
1, 2, 3, 5, 7, 11, 15, 22, 30, 42;
(End)
		

Crossrefs

Cf. A000041.

Formula

T(n,k) = A000041(k), k >= 1. - Omar E. Pol, Apr 23 2012

Extensions

Better definition from Omar E. Pol, Apr 24 2012