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A301823
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
11
0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 4, 13, 0, 5, 18, 25, 8, 34, 0, 8, 50, 74, 68, 16, 89, 0, 13, 128, 278, 299, 177, 32, 233, 0, 21, 338, 968, 1351, 1197, 457, 64, 610, 0, 34, 882, 3450, 6653, 6501, 4785, 1183, 128, 1597, 0, 55, 2312, 12210, 30441, 47363, 31061, 19130, 3075
OFFSET
1,5
COMMENTS
Table starts
.0....1...1....2......3.......5.........8.........13..........21............34
.0....2...2....8.....18......50.......128........338.........882..........2312
.0....5...4...25.....74.....278.......968.......3450.......12210.........43316
.0...13...8...68....299....1351......6653......30441......146175........682879
.0...34..16..177...1197....6501.....47363.....284691.....1896274......11958940
.0...89..32..457...4785...31061....333335....2626219....23877827.....205351902
.0..233..64.1183..19130..147954...2341241...24102055...298497818....3505205058
.0..610.128.3075..76499..705180..16471479..221373169..3746076847...60097022948
.0.1597.256.8018.305959.3364845.115975709.2034255683.47059520355.1030456894273
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 2*a(n-1)
k=4: a(n) = 6*a(n-1) -13*a(n-2) +13*a(n-3) -6*a(n-4) +a(n-5)
k=5: a(n) = 8*a(n-1) -22*a(n-2) +28*a(n-3) -17*a(n-4) +4*a(n-5) for n>7
k=6: [order 16] for n>17
k=7: [order 26] for n>28
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
n=3: [order 14] for n>18
n=4: [order 66] for n>72
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .0..0..0..0
..1..1..1..1. .1..1..0..0. .0..1..0..1. .0..1..0..0. .1..1..0..1
..0..0..1..0. .1..1..1..1. .1..0..1..1. .1..1..0..0. .1..0..1..0
..0..1..0..1. .0..0..1..1. .0..0..0..0. .1..1..0..0. .0..1..0..1
..0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1
CROSSREFS
Column 2 is A001519.
Column 3 is A000079(n-1).
Row 1 is A000045(n-1).
Row 2 is A175395(n-1).
Sequence in context: A300822 A118658 A165912 * A301999 A171936 A375372
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 27 2018
STATUS
approved