A264490 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 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

1, 1, 3, 1, 1, 4, 1, 10, 12, 12, 1, 8, 36, 16, 25, 1, 35, 108, 212, 214, 52, 1, 42, 324, 788, 2144, 324, 121, 1, 130, 972, 4772, 21466, 9714, 2960, 261, 1, 194, 2916, 23076, 217049, 142352, 92052, 6442, 576, 1, 501, 8748, 122628, 2186741, 2517024, 2870927, 581575

Offset: 1

Author

R. H. Hardin, Nov 14 2015

Keywords

• nonn
• tabl

Comments

Table starts

....1......1........1..........1...........1...........1...........1

....3......1.......10..........8..........35..........42.........130

....4.....12.......36........108.........324.........972........2916

...12.....16......212........788........4772.......23076......122628

...25....214.....2144......21466......217049.....2186741....22085009

...52....324.....9714.....142352.....2517024....42169152...714303376

..121...2960....92052....2870927....89130069..2775259622.86190450233

..261...6442...581575...30309632..1749889912.98973991195

..576..42656..4510937..463508815.47485981944

.1280.113575.31398740.5517128232

Examples

			Some solutions for n=4 k=4
..5..6..7..8..9....5..6..7..4..9....5..6..7..8..9....5..2..7..8..9
..0.11..2.13.14...10.11.12.13.14...10.11..2.13..4....0.11.12..3..4
.22.16..1..4..3...22..0..1..2..3...22..0..1.14..3...22.16..1.18.19
.20.21.18.23.24...20.21..8.23.24...20.21.18.23.24...20.21..6.23.14
.15.10.17.12.19...15.16.17.18.19...15.16.17.12.19...15.10.17.24.13
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..98

Crossrefs

Row 3 is A003946.

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) +4*a(n-5) +a(n-6) -a(n-9)

k=2: [order 36]

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = 3*a(n-2) +2*a(n-3) +a(n-4) -a(n-5)

n=3: a(n) = 3*a(n-1)

n=4: a(n) = a(n-1) +16*a(n-2) +24*a(n-3) +16*a(n-4) +32*a(n-5) +32*a(n-6)

n=5: [order 39]

n=6: [order 10] for n>11