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A317065 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 5
1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 25, 24, 1, 1, 82, 139, 139, 82, 1, 1, 272, 818, 1595, 818, 272, 1, 1, 908, 4869, 17947, 17947, 4869, 908, 1, 1, 3076, 29339, 207116, 384535, 207116, 29339, 3076, 1, 1, 10444, 177688, 2403703, 8450612, 8450612, 2403703 (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......25.......139.........818...........4869............29339

.1....24.....139......1595.......17947.........207116..........2403703

.1....82.....818.....17947......384535........8450612........186574154

.1...272....4869....207116.....8450612......354399907......14920072888

.1...908...29339...2403703...186574154....14920072888....1197129513001

.1..3076..177688..27979008..4130997988...629855730272...96317261216226

.1.10444.1078090.325990496.91552460948.26612973830635.7756014658872472

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 14] for n>16

k=4: [order 38] for n>40

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A303882.

Column 3 is A305680.

Column 4 is A305681.

Sequence in context: A305954 A317215 A305685 * A316932 A317703 A055107

Adjacent sequences:  A317062 A317063 A317064 * A317066 A317067 A317068

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 20 2018

STATUS

approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)