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A316932 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 25, 24, 1, 1, 82, 143, 143, 82, 1, 1, 272, 851, 1719, 851, 272, 1, 1, 908, 5114, 20235, 20235, 5114, 908, 1, 1, 3076, 31197, 242908, 467377, 242908, 31197, 3076, 1, 1, 10444, 191330, 2937685, 10973407, 10973407, 2937685 (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.......143..........851...........5114.............31197

.1....24.....143......1719........20235.........242908...........2937685

.1....82.....851.....20235.......467377.......10973407.........259460352

.1...272....5114....242908.....10973407......504420842.......23331389753

.1...908...31197...2937685....259460352....23331389753.....2110655397816

.1..3076..191330..35648580...6154985913..1082511783630...191524282642552

.1.10444.1175122.433015180.146148278604.50268964898040.17393755319723555

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 13] for n>15

k=4: [order 34] for n>35

k=5: [order 89] for n>92

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A303882.

Sequence in context: A317215 A305685 A317065 * A317703 A055107 A297193

Adjacent sequences:  A316929 A316930 A316931 * A316933 A316934 A316935

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 16 2018

STATUS

approved

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Last modified December 7 15:24 EST 2021. Contains 349581 sequences. (Running on oeis4.)