A317703 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6, 7 or 8 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, 468002, 242908, 31197, 3076, 1, 1, 10444, 191330, 2937685, 11013057, 11013057, 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.......468002.......11013057.........261020405

.1...272....5114....242908.....11013057......508895558.......23660712291

.1...908...31197...2937685....261020405....23660712291.....2157266427366

.1..3076..191330..35648580...6206695998..1103426578662...197276106238236

.1.10444.1175122.433015180.147728990014.51504728212214.18056111727655363

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 87] for n>90

Example

Some solutions for n=5 k=4
..0..1..1..1. .0..1..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1
..1..0..0..0. .0..1..0..1. .0..0..1..0. .0..0..1..1. .0..0..0..0
..1..0..1..1. .0..0..0..0. .0..1..1..1. .1..1..0..1. .1..0..1..1
..1..0..1..1. .1..1..1..1. .0..1..0..0. .0..0..0..1. .0..1..1..0

Crossrefs

Column 2 is A303882.

Column 3 is A316927.

Column 4 is A316928.

Sequence in context: A305685 A317065 A316932 * A055107 A297193 A272867

Adjacent sequences: A317700 A317701 A317702 * A317704 A317705 A317706

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 04 2018

Status

approved