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.

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

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