A264569 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 1,0 1,1 0,-1 or -1,1.

1, 1, 1, 1, 2, 1, 2, 4, 4, 2, 2, 8, 10, 8, 2, 4, 24, 44, 31, 16, 3, 4, 64, 143, 192, 79, 32, 4, 7, 160, 633, 1130, 888, 224, 64, 5, 9, 384, 2172, 8356, 7808, 4104, 646, 128, 7, 13, 960, 8409, 47571, 96429, 57265, 18540, 1784, 256, 9, 18, 2432, 32046, 305844, 868613

Offset: 1

Author

R. H. Hardin, Nov 17 2015

Keywords

• nonn
• tabl

Comments

Table starts

.1...1.....1.......2.........2...........4.............4...............7

.1...2.....4.......8........24..........64...........160.............384

.1...4....10......44.......143.........633..........2172............8409

.2...8....31.....192......1130........8356.........47571..........305844

.2..16....79.....888......7808.......96429........868613.........8968735

.3..32...224....4104.....57265.....1133040......16284544.......273793368

.4..64...646...18540....403872....13182464.....298587595......8004883334

.5.128..1784...85752...2873739...152082304....5442431797....235814997396

.7.256..5010..389340..20432891..1755041376...99386232806...6882481295560

.9.512.14026.1787832.144677017.20212718576.1803702025944.200087118615516

Examples

			Some solutions for n=4 k=4
..1..2..3..4..8....1..5..6..4..8....1..5..3..4..8....1..2..3..4..8
..0..7.11..9.13....0..7..2..9..3....0..7..2..9.13....0.10.11.12.13
..5..6.16.17.18...11.15.16.17.18...11..6.16.17.18....5..6..7.14..9
.10.20.21.12.14...10.20.12.13.14...10.20.21.12.14...16.20.21.19.23
.15.22.23.24.19...21.22.23.24.19...15.22.23.24.19...15.22.17.24.18
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..179

Crossrefs

Column 1 is A000931(n+4).

Column 2 is A000079(n-1).

Row 1 is A253412(n-2).

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: a(n) = 18*a(n-2) +36*a(n-3) -45*a(n-4) -216*a(n-5) -243*a(n-6) for n>7

k=5: [order 84]

k=6: [order 36] for n>40

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) +8*a(n-4)

n=3: [order 70]

n=4: [order 56]