A264364 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 0,0 0,2 1,0 or -1,-2.

1, 3, 1, 9, 6, 1, 18, 36, 13, 1, 36, 120, 169, 28, 1, 78, 400, 936, 784, 60, 1, 169, 1440, 5184, 7168, 3600, 129, 1, 364, 5184, 33408, 65536, 54720, 16641, 277, 1, 784, 18432, 215296, 730368, 831744, 418992, 76729, 595, 1, 1680, 65536, 1323792, 8139609

Offset: 1

Author

R. H. Hardin, Nov 12 2015

Keywords

• nonn
• tabl

Comments

Table starts

.1....3.......9.........18...........36.............78.............169

.1....6......36........120..........400...........1440............5184

.1...13.....169........936.........5184..........33408..........215296

.1...28.....784.......7168........65536.........730368.........8139609

.1...60....3600......54720.......831744.......16066704.......310358689

.1..129...16641.....418992.....10549504......353333680.....11834176225

.1..277...76729....3204336....133818624.....7767356736....450847788304

.1..595..354025...24514000...1697440000...170773835200..17180991840016

.1.1278.1633284..187528608..21531453696..3754476071280.654674355426025

.1.2745.7535025.1434558960.273119121664.82543032602992

Examples

			Some solutions for n=4 k=4
..0..1..2..3..4....7..8..0..3..2....0..8..2..1..4....0..1..2..3..4
.12..6..7..8..9...12..1..5..6..4...12.13.14..3..7...12..6.14..8..7
..5.18.19.11.14...17.18.10.13..9....5..6.19.11..9....5.11.10.13..9
.10.16.24.13.17...22.11.24.16.14...10.16.24.18.17...15.23.24.16.19
.15.21.20.23.22...15.21.20.23.19...15.21.20.23.22...20.21.17.18.22
		

Links

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

Crossrefs

Column 2 is A002478(n+1).

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 3*a(n-1) +28*a(n-2) +57*a(n-3) +10*a(n-4) -24*a(n-5) +8*a(n-6)

k=5: a(n) = 11*a(n-1) +22*a(n-2) -8*a(n-3)

k=6: [order 30]

Empirical for row n:

n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9)

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