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A304419 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero. 7
1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 23, 24, 1, 1, 82, 103, 103, 82, 1, 1, 272, 520, 835, 520, 272, 1, 1, 908, 2671, 7017, 7017, 2671, 908, 1, 1, 3076, 13876, 60245, 98568, 60245, 13876, 3076, 1, 1, 10444, 72399, 522349, 1389257, 1389257, 522349, 72399, 10444, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

.1.....1......1........1..........1............1..............1

.1.....4......8.......24.........82..........272............908

.1.....8.....23......103........520.........2671..........13876

.1....24....103......835.......7017........60245.........522349

.1....82....520.....7017......98568......1389257.......19831472

.1...272...2671....60245....1389257.....32181958......755715475

.1...908..13876...522349...19831472....755715475....29251894460

.1..3076..72399..4542604..283040177..17729422188..1129111647895

.1.10444.378321.39567170.4045732942.416850100691.43720181502419

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 47] for n>48

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A303882.

Sequence in context: A316376 A306136 A317271 * A316244 A305954 A317215

Adjacent sequences:  A304416 A304417 A304418 * A304420 A304421 A304422

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 12 2018

STATUS

approved

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Last modified September 20 16:30 EDT 2019. Contains 327242 sequences. (Running on oeis4.)