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A302472
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1147, 361, 0, 13, 1934, 4556, 10264, 8493, 5486, 1172, 0, 21, 6861, 21843, 78679, 101109, 53575, 25599, 3809, 0, 34, 24386, 103319, 584333, 1141147, 990266, 331044
OFFSET
1,5
COMMENTS
Table starts
.0.....1......1........2.........3...........5.............8..............13
.0.....3.....14.......45.......146.........537..........1934............6861
.0....11.....49......203.......955........4556.........21843..........103319
.0....34....250.....1401.....10264.......78679........584333.........4330427
.0...111...1147.....8493....101109.....1141147......12546601.......139759054
.0...361...5486....53575....990266....16983273.....278275383......4682106140
.0..1172..25599...331044...9731423...251512646....6145486847....156721340433
.0..3809.121626..2075845..96648626..3770915891..137317050228...5300304476103
.0.12377.572657.12918219.950374395.55956081186.3037409718914.177368160967073
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 43] for n>44
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 19] for n>21
n=4: [order 63] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .1..1..1..0. .0..0..1..1. .0..1..0..1. .1..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..0..1. .1..0..0..0. .1..1..1..1
..1..0..1..0. .1..0..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1
..0..0..0..1. .1..1..1..1. .1..1..1..0. .1..1..1..0. .1..1..1..0
CROSSREFS
Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A302225.
Sequence in context: A319501 A302224 A302670 * A303254 A256068 A302381
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 08 2018
STATUS
approved