A317733 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 161, 98, 3, 5, 383, 1250, 1250, 383, 5, 8, 1493, 9541, 19208, 9541, 1493, 8, 13, 5824, 72715, 293378, 293378, 72715, 5824, 13, 21, 22717, 554642, 4458098, 8931649, 4458098, 554642, 22717, 21, 34, 88609, 4229957

Offset

1,5

Comments

Table starts

..0.....1........1...........2.............3................5

..1.....7.......25..........98...........383.............1493

..1....25......161........1250..........9541............72715

..2....98.....1250.......19208........293378..........4458098

..3...383.....9541......293378.......8931649........270714329

..5..1493....72715.....4458098.....270714329......16360102553

..8..5824...554642....67837952....8216055128.....990049380944

.13.22717..4229957..1032124178..249314217853...59904290609773

.21.88609.32260015.15703109762.7565327218559.3624564255839937

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

k=3: a(n) = 6*a(n-1) +11*a(n-2) +11*a(n-3) -2*a(n-4) -a(n-5) -2*a(n-6)

k=4: a(n) = 12*a(n-1) +42*a(n-2) +107*a(n-3) -30*a(n-4) +12*a(n-5) -16*a(n-6)

k=5: [order 21]

k=6: [order 36]

k=7: [order 81]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A305692 A317072 A316953 * A258335 A266985 A286912

Adjacent sequences: A317730 A317731 A317732 * A317734 A317735 A317736

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 05 2018

Status

approved