|
| |
|
|
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.
|
|
14
|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
