Back to the four-dim partitions page

This page will have results from the **depth 6** run to determine the number of four-dimensional partitions for all positive integers $<=40.$

### Predictions

We make predictions for the four-dim partitions of integers, $p_4(n)$, in the range $n\in [36,40]$ using a one-parameter fit, $q_3(n)$, that is chosen to give the exact answer for $n=35$. The prediction is being made on **Sun Jul 3 16:26:10 IST 2011**. Exact numbers for 36, 37 obtained on July 4 using a depth 12 run. Results from the depth 6 run obtained on **July 13, 2011**.

$n$ | 35 | 36 | 37 | 38 | 39 | 40 |
---|---|---|---|---|---|---|

$q_4(n)$ | used for fit | 7383955608934 | 14865925276260 | 29815471230558 | 59578315944924 | 118625717447173 |

$p_4(n)$ | 3653256942840 | 7375178344373 | 14833679265311 | 29727028383070 | 59363454021280 | 118137556912895 |

### Results

This is sequence A000334 in the OEIS. Here are the results using v2.0 of the 4d code. This adds five numbers that will be eventually contributed to the OEIS.

c[N] = no. of 4d partitions of N

c[1] = 1

c[2] = 5

c[3] = 15

c[4] = 45

c[5] = 120

c[6] = 326

c[7] = 835

c[8] = 2145

c[9] = 5345

c[10] = 13220

c[11] = 32068

c[12] = 76965

c[13] = 181975

c[14] = 425490

c[15] = 982615

c[16] = 2245444

c[17] = 5077090

c[18] = 11371250

c[19] = 25235790

c[20] = 55536870

c[21] = 121250185

c[22] = 262769080

c[23] = 565502405

c[24] = 1209096875

c[25] = 2569270050

c[26] = 5427963902

c[27] = 11404408525

c[28] = 23836421895

c[29] = 49573316740

c[30] = 102610460240

c[31] = 211425606778

c[32] = 433734343316

c[33] = 886051842960

c[34] = 1802710594415

c[35] = 3653256942840

c[36] = 7375178344373

c[37] = 14833679265311

c[38] = 29727028383070

c[39] = 59363454021280

c[40] = 118137556912895

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