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A264520
T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.
12
1, 1, 0, 1, 0, 1, 2, 1, 3, 0, 4, 2, 9, 0, 1, 6, 4, 42, 36, 12, 0, 9, 8, 196, 228, 144, 0, 1, 12, 16, 644, 1444, 1644, 576, 46, 0, 16, 32, 2116, 8018, 18769, 10368, 2116, 0, 1, 24, 64, 6854, 44521, 169195, 186624, 65182, 8281, 177, 0, 36, 128, 22201, 258264, 1525225
OFFSET
1,7
COMMENTS
Table starts
.1...1......1........2..........4............6..............9...............12
.0...0......1........2..........4............8.............16...............32
.1...3......9.......42........196..........644...........2116.............6854
.0...0.....36......228.......1444.........8018..........44521...........258264
.1..12....144.....1644......18769.......169195........1525225.........14158040
.0...0....576....10368.....186624......2856816.......43731769........696507612
.1..46...2116....65182....2007889.....50099452.....1250046736......33040712340
.0...0...8281...414414...20738916....868998834....36412654041....1611878726112
.1.177..31329..2603670..216384100..14882827790..1023636039001...75733369600339
.0...0.121801.16540506.2246191236.256959272592.29395568245824.3617985452054688
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 6*a(n-2) -11*a(n-4) +13*a(n-6) -11*a(n-8) +6*a(n-10) -a(n-12)
k=3: [order 19]
k=4: [order 84]
k=5: [order 90]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3) -a(n-4) +a(n-5) +a(n-6) -a(n-9)
n=2: a(n) = 2*a(n-1)
EXAMPLE
Some solutions for n=4 k=4
..7..8..9..1..2....7..8..0..1..2....7..8..0..1..2....5..8..7..1..2
..0.13.14..3..4...10.11.14..3..4...10.11.12..3..4....0.13.14..3..4
..5..6.10.18.12....5..6.17.18..9....5..6.19.18..9...17..6.10.11..9
.20.11.22.23.24...22.23.12.13.24...20.23.24.13.14...22.21.12.23.24
.15.16.17.21.19...15.16.20.21.19...15.16.17.21.22...15.16.20.18.19
CROSSREFS
Row 1 is A224809(n+1).
Row 2 is A000079(n-3).
Sequence in context: A088002 A030109 A208571 * A058208 A070817 A231347
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 16 2015
STATUS
approved