Number of 4d partitions <=40

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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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