OFFSET

1,2

COMMENTS

The length of each row is given by A000041.

As many sequences start like the positive integers, their row sums when disposed in this shape start with the same values.

Here is a sample list by A-number order of the sequences which are sufficiently close to A000027 to have the same row sums for at least 8 terms.

EXAMPLE

Let's put the list of integers in a triangle whose rows have length p(n), number of integer partitions of n.

.

1 | 1

5 | 2 3

15 | 4 5 6

45 | 7 8 9 10 11

105 | 12 13 14 15 16 17 18

264 | 19 20 21 22 23 24 25 26 27 28 29

555 | 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

.

The sequence gives the row sums of this triangle.

MATHEMATICA

Module[{s = 0},

Table[s +=

PartitionsP[n - 1]; (s + PartitionsP[n])*(s + PartitionsP[n] - 1)/2 -

s*(s - 1)/2, {n, 1, 30}]]

CROSSREFS

KEYWORD

nonn

AUTHOR

Olivier Gérard, May 31 2024

STATUS

approved