OFFSET

0,3

COMMENTS

Number of integer partitions of n with strictly increasing run-sums. - Gus Wiseman, Oct 22 2022

FORMULA

a(n) <= A304406(n).

EXAMPLE

n | | Sequence of the sum of the same summands

--+----------------------+-----------------------------------------

1 | 1 | 1

2 | 2 | 2

| 1+1 | 2

3 | 3 | 3

| 1+1+1 | 3

4 | 4 | 4

| 2+2 | 4

| 1+1+1+1 | 4

5 | 5 | 5

| 2+1+1+1 | 3, 2

| 1+1+1+1+1 | 5

6 | 6 | 6

| 3+3 | 6

| 2+2+2 | 6

| 2+1+1+1+1 | 4, 2

| 1+1+1+1+1+1 | 6

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Less@@Total/@Split[#]&]], {n, 0, 30}] (* Gus Wiseman, Oct 22 2022 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 12 2018

STATUS

approved