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A264583
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,-1 1,2 or -1,1.
13
0, 1, 1, 0, 2, 0, 1, 4, 4, 0, 1, 10, 4, 8, 1, 1, 16, 28, 6, 16, 0, 3, 56, 97, 104, 25, 32, 0, 1, 128, 333, 553, 505, 68, 64, 1, 3, 320, 1380, 2232, 3668, 2144, 112, 128, 0, 6, 784, 4497, 21312, 30718, 24370, 8185, 281, 256, 0, 5, 1792, 16712, 86812, 366292, 314166
OFFSET
1,5
COMMENTS
Table starts
.0...1....0......1........1..........1...........3...........1...........3
.1...2....4.....10.......16.........56.........128.........320.........784
.0...4....4.....28.......97........333........1380........4497.......16712
.0...8....6....104......553.......2232.......21312.......86812......553861
.1..16...25....505.....3668......30718......366292.....2509523....26091488
.0..32...68...2144....24370.....314166.....5469993....64600334...955403058
.0..64..112...8185...145761....2561017....80571013..1370091018.31774873994
.1.128..281..33056...905291...24729380..1220343344.31418295732
.0.256..856.141037..5678975..248623843.18239876421
.0.512.1674.570758.35331350.2294091610
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-3)
k=2: a(n) = 2*a(n-1)
k=3: [order 15]
k=4: a(n) = 2*a(n-1) +36*a(n-3) +9*a(n-4) -243*a(n-6) for n>7
k=5: [order 84]
k=6: [order 36] for n>40
Empirical for row n:
n=1: a(n) = a(n-3) +a(n-4) +2*a(n-5) -a(n-9) -a(n-10)
n=2: a(n) = 2*a(n-1) +16*a(n-5) -16*a(n-6) +32*a(n-7) -64*a(n-10)
EXAMPLE
Some solutions for n=4 k=4
..1..2..3..7..8....1..2..3..4..8....1..2..3..7..8....1..5..3..4..8
..0.10.11.12..4....0..7.11..9.13....0.10.11..9..4....6.10..0..9..2
..5.15.13..6..9....5..6.16.14.18....5.15.13..6.18...11.15..7.17.18
.16.20.18.19.14...10.20.12.19.23...16.20.12.19.14...16.20.12.13.14
.21.22.23.24.17...21.22.15.24.17...21.22.23.24.17...21.22.23.24.19
CROSSREFS
Column 2 is A000079(n-1).
Sequence in context: A342321 A098689 A288515 * A158984 A158417 A139435
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 18 2015
STATUS
approved