A263389 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..n*k-1 with each element moved a city block distance of exactly 2.

1, 4, 4, 16, 144, 16, 36, 1600, 1600, 36, 169, 17376, 70225, 17376, 169, 576, 240100, 2205225, 2205225, 240100, 576, 2025, 3187140, 85599504, 188020096, 85599504, 3187140, 2025, 7056, 40513225, 3623076864, 24782315776, 24782315776

Offset

1,2

Comments

Table starts

....1........4.........16..........36.........169...........576.........2025

....4......144.......1600.......17376......240100.......3187140.....40513225

...16.....1600......70225.....2205225....85599504....3623076864.146943422224

...36....17376....2205225...188020096.24782315776.3447945608640

..169...240100...85599504.24782315776

..576..3187140.3623076864

.2025.40513225

.7056

Links

R. H. Hardin, Table of n, a(n) for n = 1..40

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-2) +15*a(n-3) +35*a(n-4) +25*a(n-5) +5*a(n-6) -5*a(n-7) -25*a(n-8) -35*a(n-9) -15*a(n-10) -5*a(n-11) +a(n-13)

Example

Some solutions for n=3 k=4
..2..3..0..7.14....2..3.12..1..8....2..3..0..9.14....2..5..6..1.14
.11..8..1..4.13....7.10.11..6.19...11..8..5..4..7....7..8.13.18..3
.12..5..6.19.18....0.17.16..9..4...12..1.10.19.18....0.15.10..9..4
.17.10.15.16..9....5.18.15.14.13...17..6.15.16.13...11.12.19.16.17

Crossrefs

Sequence in context: A284494 A091541 A094354 * A019062 A019013 A340425

Adjacent sequences: A263386 A263387 A263388 * A263390 A263391 A263392

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 16 2015

Status

approved