Partition function (number theory): Difference between revisions

Revision as of 21:31, 15 February 2023

Revision as of 21:35, 15 February 2023

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|+ Example values of q(n) and associated partitions

|-

! ''n'' || ''q''(''n'') || PartitionsStrict without repeated partspartitions

!Partitions with only odd parts

|-

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|() empty partition

|-

| 1 || 1 || (1)

|(1)

|-

| 2 || 1 || (2)

|(1+1)

|-

| 3 || 2 || (1+2), (3)

|(1+1+1), (3)

|-

| 4 || 2 || (1+3), (4)

|(1+1+1+1), (1+3)

|-

| 5 || 3 || (2+3), (1+4), (5)

|(1+1+1+1+1), (1+1+3), (5)

|-

| 6 || 4|| (1+2+3), (2+4), (1+5), (6)

|(1+1+1+1+1+1), (1+1+1+3), (3+3), (1+5)

|-

|7

|5

|(1+2+4), (3+4), (2+5), (1+6), (7)

|(1+1+1+1+1+1+1), (1+1+1+1+3), (1+3+3), (1+1+5), (7)

|-

|8

|6

|(1+3+4), (1+2+5), (3+5), (2+6), (1+7), (8)

|(1+1+1+1+1+1+1+1), (1+1+1+1+1+3), (1+1+3+3), (1+1+1+5), (3+5), (1+7)

|-

|9

|8

|(2+3+4), (1+3+5), (4+5), (1+2+6), (3+6), (2+7), (1+8), (9)

|1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+3, 1+1+1+3+3, 3+3+3, 1+1+1+1+5, 1+3+5, 1+1+7, 9

|......

|-

|10

|10

|(1+2+3+4), (2+3+5), (1+4+5), (1+3+6), (4+6), (1+2+7), (3+7), (2+8), (1+9), (10)

|......

|}