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

1,3

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

Links

Table of n, a(n) for n=1..88.

Formula

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

Example

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.

Sequence in context: A066657 A119444 A060040 * A264482 A193588 A165884

Adjacent sequences: A092077 A092078 A092079 * A092081 A092082 A092083

Keyword

nonn,tabl,easy

Author

Wolfdieter Lang, Mar 19 2004

Extensions

Better definition from Omar E. Pol, Apr 24 2012

Status

approved