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A282996 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors. 7
2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 163, 98, 24, 44, 291, 803, 803, 291, 44, 81, 865, 3971, 6547, 3971, 865, 81, 149, 2570, 19587, 53389, 53389, 19587, 2570, 149, 274, 7637, 96693, 435027, 720417, 435027, 96693, 7637, 274, 504, 22693, 477297, 3546870 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...2.....4........7.........13...........24.............44...............81

...4....11.......33.........98..........291............865.............2570

...7....33......163........803.........3971..........19587............96693

..13....98......803.......6547........53389.........435027..........3546870

..24...291.....3971......53389.......720417........9706901........130854309

..44...865....19587.....435027......9706901......216173426.......4817792042

..81..2570....96693....3546870....130854309.....4817792042.....177509416175

.149..7637...477297...28911809...1763845523...107354061547....6539125324144

.274.22693..2355925..235681253..23775564134..2392171690343..240894164469261

.504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..312

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)

k=3: [order 9]

k=4: [order 15]

k=5: [order 36]

k=6: [order 69]

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0

..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1

..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0

..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0

..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0

CROSSREFS

Column 1 is A000073(n+3).

Diagonal is A067968.

Sequence in context: A282862 A296578 A268750 * A295275 A295253 A295652

Adjacent sequences:  A282993 A282994 A282995 * A282997 A282998 A282999

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 26 2017

STATUS

approved

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Last modified October 23 11:41 EDT 2021. Contains 348212 sequences. (Running on oeis4.)