A264506 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 0,-1 0,1 or 1,0.

1, 1, 2, 3, 2, 3, 6, 14, 4, 4, 12, 38, 46, 8, 6, 24, 137, 211, 149, 16, 9, 46, 432, 1235, 1224, 524, 32, 13, 91, 1417, 6613, 11464, 7177, 1790, 64, 19, 177, 4554, 35356, 105324, 110185, 41622, 6084, 128, 28, 349, 14710, 190821, 934515, 1697577, 1041411, 241432

Offset

1,3

Comments

Table starts

..1...1......3........6.........12............24..............46

..2...2.....14.......38........137...........432............1417

..3...4.....46......211.......1235..........6613...........35356

..4...8....149.....1224......11464........105324..........934515

..6..16....524.....7177.....110185.......1697577........24950224

..9..32...1790....41622....1041411......26941396.......655642859

.13..64...6084...241432....9813822.....427111736.....17171750212

.19.128..20812..1401492...92711566....6776356720....450129538653

.28.256..71127..8132167..875322080..107417903076..11788157463588

.41.512.242856.47182878.8261489271.1702319756800.308570749630453

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 14]

k=4: a(n) = 6*a(n-1) -5*a(n-2) +36*a(n-3) -72*a(n-4) -243*a(n-6) for n>7

k=5: [order 84]

k=6: [order 36] for n>38

Empirical for row n:

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

n=2: [order 14]

n=3: [order 69]

Example

Some solutions for n=4 k=4
..1..0..3..2..8....1..2..6..4..3....1..2..3..4..8....1..0..3..4..8
..6.10.11..9..4....0.10.11..9..8....0..7.11.12.13....6..7..2..9.13
..5.12..7.14.13....5.12..7.17.13....5..6.16.14..9....5.10.11.14.18
.16.20.18.17.23...16.20.18.19.14...10.20.21.19.18...16.20.12.17.23
.15.22.21.24.19...15.22.21.24.23...15.22.17.24.23...15.22.21.24.19

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A000079(n-1).

Sequence in context: A215412 A227585 A038063 * A085204 A228527 A055375

Adjacent sequences: A264503 A264504 A264505 * A264507 A264508 A264509

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2015

Status

approved