[seqfan] Re: Permutations along all diagonals and subdiagonals

[Ron Hardin]

Good, I'll add it.  Try the nX4, in full
4 0
5 1
6 0
7 25
8 0
9 289
10 0
11 2025
12 0
13 16641
14 0
15 145161
16 0
17 1185921
18 0
19 9715689
20 0
21 80874049
22 0
23 668377609
24 0
25 5516478529
26 0
27 45630513769
28 0
29 377252695681
30 0
31 3117897783049
32 0
33 25774558228225
34 0
35 213069752354281
36 0
37 1761278190732225
38 0
39 14559352270703881
40 0
41 120353686919843521
42 0
43 994886771041931881
44 0
45 8224096611228604929
46 0
47 67983481298460902409
48 0
49 561976684516349130625
50 0
51 4645507264493472159721
52 0
53 38401490333536696238401
54 0
55 317440983764793148886025
56 0
57 2624084996956950437714241
58 0
59 21691661060460519328032361
60 0
61 179311325821701804976122241
62 0
63 1482254000523300302593864969
64 0
65 12252861976216945210014409729
66 0
67 101286707047001841076987039209
68 0
69 837273531453172070855080198849
70 0
71 6921213917946087109850716000009
72 0
73 57213324326506881333875742459841
74 0
75 472946584093340450030892997189225
76 0
77 3909552084865374953308557959380225
78 0
79 32317809280489790235451369639062025
80 0
81 267151012191157641904339743626884225
82 0
83 2208369468830127561685438749377538025
84 0
85 18255202070438889937126205035478779969
86 0
87 150904279078410923904730373124897461769
88 0
89 1247430806643192813159841682124532734529
90 0
91 10311726260288547320004358832696999279209
92 0
93 85240558354710306366767624821397285508225
94 0
95 704630108016361685030762574592170665304841
96 0
97 5824734125474157207329634244808964022053121
98 0
99 48149415198812206824852504759260414808155625



 rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: Alois Heinz <heinz at hs-heilbronn.de>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Tue, July 27, 2010 9:13:12 AM
> Subject: [seqfan] Re: Permutations along all diagonals and subdiagonals
> 
> Ron Hardin schrieb:
> > Here's three series out of it, I  guess
> >
> > %S XXX  0,1,4,9,12,25,60,121,220,441,924,1849,3612,7225,14620,29241,58140,
> > %T  XXX  
>116281,233244,466489,931612,1863225,3729180,7458361,14911260,29822521,
> >  %U XXX  
>59655964,119311929,238602012,477204025,954451740,1908903481,3817719580
> >  %N XXX Number of nX3 arrays with every diagonal and anti-diagonal of length 
>L 
>
> > containing a permutation of 1..L
> >  
> This sequence seems  to have a simple gf:
>    -(-x-2*x^2-2*x^3+4*x^4)*x^3 /  (1-2*x+x^2-2*x^3-2*x^4+4*x^5)
> 
> Alois
> 
> 
> 
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