A263964 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 1,1 or 1,2.

4, 20, 9, 108, 141, 25, 465, 2089, 1685, 64, 2265, 23841, 95161, 16856, 169, 10920, 283641, 3801496, 3232688, 183229, 441, 52752, 3408145, 180329601, 406984645, 123067561, 1926873, 1156, 253176, 40723017, 8793791605, 64094922409

Offset: 1

Author

R. H. Hardin, Oct 30 2015

Keywords

• nonn
• tabl

Comments

Table starts

....4........20..........108...........465...........2265..........10920

....9.......141.........2089.........23841.........283641........3408145

...25......1685........95161.......3801496......180329601.....8793791605

...64.....16856......3232688.....406984645....64094922409.10425268139552

..169....183229....123067561...51140612201.29721673646857

..441...1926873...4487054905.6038706224797

.1156..20563180.165950022876

.3025.218090365

.7921

Examples

			Some solutions for n=3 k=4
..0..8..6..7..4....0..1..8..6..7....0..8..9..3..4....0..1..6..9..8
..5..3..1..2.12....5..2..3..4.13....5..6..1.12..2....5..2..7..4..3
.10.11..9.16.18...10.11.15..9.18...10.11.18..7.17...10.17.12.13.14
.15.13.17.14.19...12.16.17.14.19...15.16.13.14.19...15.16.11.18.19
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..48

Crossrefs

Column 1 is A007598(n+2).

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) +40*a(n-2) -119*a(n-3) -124*a(n-4) +240*a(n-5)

k=3: [order 15]

k=4: [order 82]

Empirical for row n:

n=1: [linear recurrence of order 22]

n=2: [order 28] for n>30