The first 47 terms of A001168, from Don Knuth
Jan 9, 2001
Dear Neil,
I've got further news re sequence A001168: My old program POLYENUM
is now obsoleted by a new program POLYNUM, which implements Jensen's
algorithm with a few refinements. The URL is still the same as before.
With the new program I extended the enumeration to n=47, and verified
all of Jensen's results thru n=46. Since his algorithm is nontrivial,
I was expecting in fact that our results would NOT agree; many
possibilities for subtle errors exist, including errors that would
not show up for small n. Thus the fact that we got identical values
is reasonably convincing that the numbers are correct.
And here are those numbers:
1
2
6
19
63
216
760
2725
9910
36446
135268
505861
1903890
7204874
27394666
104592937
400795844
1540820542
5940738676
22964779660
88983512783
345532572678
1344372335524
5239988770268
20457802016011
79992676367108
313224032098244
1228088671826973
4820975409710116
18946775782611174
74541651404935148
293560133910477776
1157186142148293638
4565553929115769162
18027932215016128134
71242712815411950635
281746550485032531911
1115021869572604692100
4415695134978868448596
17498111172838312982542
69381900728932743048483
275265412856343074274146
1092687308874612006972082
4339784013643393384603906
17244800728846724289191074
68557762666345165410168738
272680844424943840614538634
The program is a fairly good test of memory --- it needs something like
850 MB of RAM and about 10 GB of disk --- and takes about a week to run.
I ran it twice, on two different machines. (Actually on five different
machines, three of which proved to be flaky! That's what I meant about
it being a fairly good test of memory.)
Depending on how long Moore's law holds up, we can expect
slightly more than one new value per year (always computed in a week, of
course), for the next ten years. After that my data structure will need
24 bytes per node instead of 20....
Don