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A298575 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 8
1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 8, 1, 8, 1, 1, 36, 2, 2, 36, 1, 1, 52, 14, 3, 14, 52, 1, 1, 100, 10, 41, 41, 10, 100, 1, 1, 356, 12, 38, 480, 38, 12, 356, 1, 1, 628, 72, 70, 374, 374, 70, 72, 628, 1, 1, 1220, 82, 374, 1055, 174, 1055, 374, 82, 1220, 1, 1, 3668, 90, 664, 9880, 604 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

.1...4..4...8....36...52...100....356....628....1220.....3668......7268

.1...4..1...2....14...10....12.....72.....82......90......400.......600

.1...8..2...3....41...38....70....374....664....1327.....4668.....10974

.1..36.14..41...480..374..1055...9880..11792...31779...239375....376486

.1..52.10..38...374..174...604...5381...5527...16221...110018....190453

.1.100.12..70..1055..604..2888..28278..43961..164865..1297974...3202666

.1.356.72.374..9880.5381.28278.582062.684296.3320171.49103067..98469245

.1.628.82.664.11792.5527.43961.684296.939451.6179745.77845252.205903671

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: a(n) = 7*a(n-3) +2*a(n-4) +a(n-5) -10*a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) with g.f. (1+3*x^2-8*x^3)/(1-x-8*x^3+4*x^4).

k=4: [order 32] for n>33

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Sequence in context: A204028 A106314 A152716 * A326039 A183374 A176263

Adjacent sequences:  A298572 A298573 A298574 * A298576 A298577 A298578

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 22 2018

STATUS

approved

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Last modified October 3 18:24 EDT 2022. Contains 357237 sequences. (Running on oeis4.)