[seqfan] Re: A077057 and A077058

[Susanne Wienand]

Dear seqfans,

I compared the first 52 values of A077057 to (A0078358 + A077058) / 2. It
did not match for n = 9 and for n = 33. Can this be typos?

 n         A0078358  A077058  (A0078358+A077058) / 2  A077057
-----------------------------------------------------------------------------------------------
  1               1               1
1                             1
  2               3               1
2                             2
  3               8               2
5                             5
  4               5               1
3                             3
  5               5               1
3                             3
  6             46               8
27                           27
  7             12               2
7                             7
  8             64             10
37                           37
  9               7               1
4                             3*
10               7               1
4                             4
11            302             40                171
171
12             39               5
22                           22
13             16               2
9                             9
14             25               3
14                           14
15          2136           250               1193                       1193
16               9               1
5                            5
17               9               1
5                            5
18         1000            106                 553
553
19             29               3
16                          16
20       11208           1138               6173                       6173
21             20               2
11                          11
22             82               8
45                          45
23           261             25                  143
143
24         1552           146                  849
849
25             11               1
6                            6
26             11               1
6                            6
27       33710         2968               18339                     18339
28           173             15
94                           94
29         3488           298                1893                       1893
30           190             16
103                         103
31             24               2
13                           13
32             61               5
33                           33
33         4354           352                 2353
2001*
34           213             17
115                         115
35       23550          1856              12703                      12703
36             13               1
7                             7
37             13               1
7                             7
38     124846          9384               67115                      67115
39         1305             97                  701
701
40           136             10
73                           73
41           110               8
59                           59
42   3528264       253970           1891117                   1891117
43             28               2
15                           15
44   1030190         72664            551427                    551427
45             43               3
23                           23
46       93102          6440             49771                      49771
47             73               5
39                           39
48   7688126     521904            4105015                  4105015
49             15               1
8                            8
50             15               1
8                            8
51       46312         3034              24673                     24673
52             77               5
41                           41

Regards,
Susanne Wienand

2012/10/3 Jean-François Alcover <jf.alcover at gmail.com>

> Dear SeqFans,
>
> I'm checking A077057 and A077058 with Mathematica,
> and I get a few cases where the equation seems not to hold :
>
> aa = A077057 =
> {1, 2, 5, 3, 3, 27, 7, 37, 3, 4, 171, 22, 9, 14,
>  1193, 5, 5, 553, 16, 6173, 11, 45, 143, 849, 6, 6, 18339,
>  94, 1893, 103, 13, 33, 2001, 115, 12703, 7, 7, 67115,
>  701, 73, 59, 1891117, 15, 551427, 23, 49771, 39, 4105015,
>  8, 8, 24673, 41, 75585293, 22, 9095891, 989, 17};
>
> bb = A077058 =
> {1, 1, 2, 1, 1, 8, 2, 10, 1, 1, 40, 5, 2, 3, 250,
>  1, 1, 106, 3, 1138, 2, 8, 25, 146, 1, 1, 2968, 15, 298, 16,
>  2, 5, 352, 17, 1856, 1, 1, 9384, 97, 10, 8, 253970, 2,
>  72664, 3, 6440, 5, 521904, 1, 1, 3034, 5, 9148450, 3,
>  1084152, 117, 2};
>
> g[n_] := Ceiling[Sqrt[n]] + n - 1;
>
> t = Table[{n, aa[[n]], bb[[n]],
>  aa[[n]]^2 - aa[[n]]*bb[[n]] - g[n]*bb[[n]]^2}, {n, 1, 57}];
>
> Select[t, Last[#] != 1 && Last[#] != -1 &]
>
> {{9, 3, 1, -5}, {33, 2001, 352, -1408703}, {54, 22, 3, -131}}
>
> Can someone explain ?
>
> jfa
>
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