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A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1637, 1652, 512, 32, 64, 2048, 11814, 21625, 11980, 2048, 64, 128, 8192, 85268, 285613, 286631, 86916, 8192, 128, 256, 32768, 615589, 3778433, 6947036, 3798398, 630604, 32768, 256, 512, 131072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1......2........4..........8............16..............32
...2......8.......32........128...........512............2048
...4.....32......228.......1637.........11814...........85268
...8....128.....1652......21625........285613.........3778433
..16....512....11980.....286631.......6947036.......168799572
..32...2048....86916....3798398.....168833401......7530280825
..64...8192...630604...50347423....4104946296....336148647504
.128..32768..4575332..667361051...99807877377..15005851329729
.256.131072.33196332.8845980434.2426739457531.669868217032865
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +2*a(n-2) +2*a(n-3) -20*a(n-4) -16*a(n-5)
k=4: [order 15]
k=5: [order 46]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 7*a(n-1) +4*a(n-2) -17*a(n-3) -3*a(n-4) -9*a(n-6) +14*a(n-7) for n>8
n=4: [order 15] for n>16
n=5: [order 64] for n>65
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..0..0. .0..0..1..0
..1..0..0..0. .1..1..0..1. .0..0..1..0. .1..1..0..0. .1..1..1..1
..0..0..1..0. .1..1..0..1. .0..0..1..1. .0..1..1..1. .1..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A004171(n-1).
Sequence in context: A299661 A320371 A317565 * A300215 A300804 A303456
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 12 2018
STATUS
approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)