A264272 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

4, 10, 9, 25, 48, 25, 65, 256, 305, 64, 169, 1280, 3721, 1800, 169, 442, 6400, 40626, 50625, 10933, 441, 1156, 32000, 443556, 1143000, 707281, 65856, 1156, 3026, 160000, 4861800, 25806400, 33729146, 9834496, 397970, 3025, 7921, 800000, 53290000

Offset: 1

Author

R. H. Hardin, Nov 10 2015

Keywords

• nonn
• tabl

Comments

Table starts

....4......10.........25...........65.............169................442

....9......48........256.........1280............6400..............32000

...25.....305.......3721........40626..........443556............4861800

...64....1800......50625......1143000........25806400..........600090240

..169...10933.....707281.....33729146......1608491236........80568542340

..441...65856....9834496....981994496.....98054154496.....10563801093680

.1156..397970..137007025..28735927165...6027088830169...1398071103483637

.3025.2402455.1908029761.839596650695.369450492999025.184549492112860840

Examples

			Some solutions for n=3 k=4
..5..8..7..3..4....5..1..9..3..4....0..8..2..3..4....0..8..2..3..9
..0..6..2..1.14....0.11..2..8.14....5.13.14..1..9....5..1.12.13..4
.10.18.19.13..9...10.18..7..6.19...15.16.12..6..7...15.16..7..6.19
.15.16.17.11.12...15.16.17.13.12...10.11.17.18.19...10.11.17.18.14
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A007598(n+2).

Row 1 is A166516(n+2).

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

k=2: [order 8]

k=3: a(n) = 14*a(n-1) +14*a(n-2) -210*a(n-3) +210*a(n-5) -14*a(n-6) -14*a(n-7) +a(n-8)

k=4: [order 52]

k=5: [order 96]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -3*a(n-3) +a(n-4)

n=2: a(n) = 5*a(n-1) for n>3

n=3: [order 22]

n=4: [order 25] for n>27