A316953 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 160, 98, 3, 5, 383, 1240, 1240, 383, 5, 8, 1493, 9417, 18956, 9417, 1493, 8, 13, 5824, 71505, 287292, 287292, 71505, 5824, 13, 21, 22717, 543155, 4335826, 8641499, 4335826, 543155, 22717, 21, 34, 88609, 4125662

Offset

1,5

Comments

Table starts

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

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

..1....25......160........1240..........9417............71505

..2....98.....1240.......18956........287292..........4335826

..3...383.....9417......287292.......8641499........259163370

..5..1493....71505.....4335826.....259163370......15440641209

..8..5824...543155....65510494....7779344498.....920789559090

.13.22717..4125662...989703110..233495963949...54906173292280

.21.88609.31337363.14951804382.7008276669223.3273992108473660

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

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) +10*a(n-2) +15*a(n-3) +8*a(n-4) +3*a(n-5) +a(n-6) +2*a(n-7)

k=4: [order 13]

k=5: [order 33]

k=6: [order 76]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A317222 A305692 A317072 * A317733 A258335 A266985

Adjacent sequences: A316950 A316951 A316952 * A316954 A316955 A316956

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 17 2018

Status

approved