A092080 - OEIS

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

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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, 2;

1, 2, 3;