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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