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A302877
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 17, 10, 16, 13, 31, 35, 37, 21, 32, 21, 113, 72, 95, 82, 42, 64, 34, 363, 241, 306, 285, 209, 86, 128, 55, 813, 722, 1442, 1197, 858, 536, 179, 256, 89, 1751, 1821, 5871, 7580, 4849, 2938, 1549, 370, 512, 144, 5001, 4863, 21832, 41498
OFFSET
1,2
COMMENTS
Table starts
...1...2....3.....5......8.......13........21..........34...........55
...2...3...11....21.....31......113.......363.........813.........1751
...4...6...17....35.....72......241.......722........1821.........4863
...8..10...37....95....306.....1442......5871.......21832........89400
..16..21...82...285...1197.....7580.....41498......224087......1300510
..32..42..209...858...4849....45897....359518.....2795440.....24612087
..64..86..536..2938..23037...320405...3780984....44148194....588417750
.128.179.1549.11126.114810..2489823..44888558...786125894..15974455418
.256.370.4513.44216.603229.20679119.569313013.14827387374.460770487307
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 56] for n>59
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 60] for n>64
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1
..1..0..1..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..1..0..1
..1..0..1..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..1..0..1
..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..1
..1..1..0..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .1..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.
Sequence in context: A059185 A302309 A303040 * A303525 A368643 A133948
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 15 2018
STATUS
approved