[seqfan] Equal-Sum Free
Ron Hardin
rhhardin at att.net
Fri Aug 3 20:08:24 CEST 2012
Analogous to square-free series http://oeis.org/A006156, consider equal-sum free
(so 1 3 1 3 is omitted, but also 1 3 3 1 and 2 2 1 3)
The column 1, 2 and 3 are finite. Question: are all columns finite? It's
doubtful I can compute column 4 far enough to tell.
T(n,k)=Number of arrays of n 0..k integers with no sum of consecutive elements
equal to a disjoint adjacent sum of an equal number of elements
Table starts
.2..3....4......5........6.........7.........8..........9.........10........11
.2..6...12.....20.......30........42........56.........72.........90.......110
.2.12...36.....80......150.......252.......392........576........810......1100
.0.18...88....276......664......1366......2512.......4264.......6800.....10330
.0.30..216....954.....2940......7404.....16092......31560......57072.....96990
.0.30..440...2898....11756.....36864.....95832.....219092.....452368....864810
.0.18..896...8808....46972....183438....570460....1520506....3584736...7709744
.0..0.1626..24014...172046....848802...3191034....9990182...27052236..65759590
.0..0.2980..65462...630456...3931086..17862744...65678336..204247760.561117076
.0..0.4692.160670..2139436..17086156..94691966..411561564.1477403080..........
.0..0.7214.394750..7274062..74389138.502572562.2581475090.....................
.0..0.8998.892432.23194018.306910564..........................................
column 3:
1 4
2 12
3 36
4 88
5 216
6 440
7 896
8 1626
9 2980
10 4692
11 7214
12 8998
13 10964
14 11174
15 11588
16 11280
17 11340
18 11294
19 11148
20 10422
21 10100
22 9174
23 8236
24 6804
25 5852
26 4934
27 4208
28 3254
29 2736
30 2186
31 1872
32 1632
33 1384
34 1008
35 952
36 960
37 964
38 968
39 976
40 880
41 784
42 448
43 324
44 208
45 172
46 144
47 104
48 64
49 32
50 16
51 0
52 0
rhhardin at mindspring.com
rhhardin at att.net (either)
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