A317604 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 100, 65, 16, 32, 192, 435, 435, 192, 32, 64, 569, 1959, 3047, 1959, 569, 64, 128, 1709, 8872, 20805, 20805, 8872, 1709, 128, 256, 5162, 40080, 143866, 218043, 143866, 40080, 5162, 256, 512, 15663, 181116, 994993, 2349106

Offset

1,2

Comments

Table starts

...1.....2......4........8.........16...........32.............64

...2.....8.....23.......65........192..........569...........1709

...4....23....100......435.......1959.........8872..........40080

...8....65....435.....3047......20805.......143866.........994993

..16...192...1959....20805.....218043......2349106.......25248997

..32...569...8872...143866....2349106.....40015089......679103465

..64..1709..40080...994993...25248997....679103465....18167894481

.128..5162.181116..6892556..271168201..11512061359...485582717996

.256.15663.818827.47747495.2915768974.195586936443.13027760526423

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5

k=3: [order 16] for n>17

k=4: [order 57] for n>59

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A305593 A317011 A316876 * A038208 A240484 A240636

Adjacent sequences: A317601 A317602 A317603 * A317605 A317606 A317607

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 01 2018

Status

approved