A264676 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,-1 1,0 -1,-2 -2,-2 or 0,1.

0, 1, 1, 1, 2, 0, 1, 10, 9, 0, 1, 29, 34, 19, 1, 3, 75, 123, 145, 44, 0, 3, 201, 748, 890, 603, 108, 0, 4, 588, 3698, 9205, 6851, 2417, 264, 1, 6, 1700, 17443, 88687, 123222, 43131, 9976, 649, 0, 9, 4785, 84737, 714235, 2025372, 1449467, 291315, 40825, 1573, 0, 12

Offset: 1

Author

R. H. Hardin, Nov 20 2015

Keywords

• nonn
• tabl

Comments

Table starts

.0....1......1........1...........1.............3..............3

.1....2.....10.......29..........75...........201............588

.0....9.....34......123.........748..........3698..........17443

.0...19....145......890........9205.........88687.........714235

.1...44....603.....6851......123222.......2025372.......29875350

.0..108...2417....43131.....1449467......43095017.....1095840260

.0..264...9976...291315....17406354.....918298857....40765995197

.1..649..40825..1980287...209749118...19297801298..1494347569074

.0.1573.166985.13199209..2503676777..404856272120.54204721906375

.0.3837.684253.88670692.29934965340.8489260394876

Examples

			Some solutions for n=4 k=4
..6..8..1..2..3....7..8..1..2..3...12..8..1..2..3...12.13..1..2..3
..0..5.14..7..4....0.13..6.14..4....0..5..6..7..4....0.18.19..7..4
.16.10.24.19..9....5.23.24.12..9...17.18.24.19..9....5..6.24..8..9
.21.11.12.13.18...10.11.16.17.18...10.11.16.13.14...10.11.16.17.14
.15.20.17.22.23...15.20.21.22.19...15.20.21.22.23...15.20.21.22.23
		

Links

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

Crossrefs

Row 1 is A080013(n+1).

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +a(n-3) +3*a(n-4) +2*a(n-5) -a(n-6) +4*a(n-7) -a(n-8) -a(n-10)

k=3: [order 15]

k=4: [order 26] for n>27

Empirical for row n:

n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)

n=2: [order 9]

n=3: [order 70]

n=4: [order 81] for n>86