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.

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

R. H. Hardin, Table of n, a(n) for n = 1..160

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

Adjacent sequences: A264517 A264518 A264519 * A264521 A264522 A264523

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 16 2015

Status

approved