A189155 -id:A189155 - cp's OEIS frontend

A189905 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 1 diagonally, vertically, antidiagonally or horizontally.

2, 4, 4, 8, 16, 8, 15, 64, 64, 15, 28, 225, 512, 225, 28, 52, 784, 3375, 3375, 784, 52, 96, 2704, 21952, 35656, 21952, 2704, 96, 177, 9216, 140608, 372850, 377517, 140608, 9216, 177, 326, 31329, 884736, 3833322, 6442436, 3810503, 884736, 31329, 326, 600

Offset: 1

R. H. Hardin May 01 2011

Table starts
...2......4.........8..........15............28..............52
...4.....16........64.........225...........784............2704
...8.....64.......512........3375.........21952..........140608
..15....225......3375.......35656........372850.........3833322
..28....784.....21952......377517.......6442436.......109264923
..52...2704....140608.....3810503.....101895401......2719427244
..96...9216....884736....36890502....1518596226.....63149685928
.177..31329...5545233...354894796...22333076803...1435483321366
.326.106276..34645976..3368920072..319934642768..31396505039678
.600.360000.216000000.31765314572.4537262993168.678724157124848

			Some solutions for 6X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..1....0..1..1..0....1..1..0..0....0..1..0..0....0..0..0..0
..0..0..0..0....0..1..0..1....0..0..1..0....0..0..0..0....0..0..0..0
..0..0..0..0....1..0..1..0....1..0..0..0....0..1..1..0....1..1..0..0
..1..0..1..0....0..0..0..1....0..0..1..0....0..1..0..0....0..0..0..1
..0..0..0..0....1..0..1..0....0..1..0..0....1..0..0..1....1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..144

Row 1 and Column 1 are A008937(n+1)
Row 2 and Column 2 are A189154
Row 3 and Column 3 are A189155

A250574 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with nondecreasing maximum of every three consecutive values in every row and column.

Original entry on oeis.org

512, 3375, 3375, 21952, 39852, 21952, 140608, 463006, 463006, 140608, 884736, 5281190, 9583440, 5281190, 884736, 5545233, 59025322, 194160522, 194160522, 59025322, 5545233, 34645976, 656805747, 3844025984, 6967413024, 3844025984

Offset: 1

R. H. Hardin, Nov 25 2014

Table starts
.......512........3375..........21952............140608..............884736
......3375.......39852.........463006...........5281190............59025322
.....21952......463006........9583440.........194160522..........3844025984
....140608.....5281190......194160522........6967413024........243722971680
....884736....59025322.....3844025984......243722971680......15037777879872
...5545233...656805747....75733658665.....8480014708481.....922491768788283
..34645976..7283102949..1486288137310...293803461491618...56336934011827612
.216000000.80572967431.29093999130722.10151010566609616.3430565103477146672

			Some solutions for n=2 k=4
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..1..0..1..0..1..0....0..1..1..0..1..0....1..0..0..1..1..1....0..0..0..1..1..0
..1..0..1..1..1..0....0..0..0..1..0..0....0..0..1..0..0..1....0..0..0..0..0..0
..0..1..1..0..0..1....1..1..1..0..0..1....1..0..0..1..0..1....1..1..0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..126

Column 1 is A189155(n+2)

Empirical for column k:
k=1: [linear recurrence of order 19]
k=2: [order 49]

cp's OEIS Frontend

A189905 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 1 diagonally, vertically, antidiagonally or horizontally.

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