A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 6, 5, 8, 13, 8, 13, 13, 8, 13, 21, 15, 26, 31, 26, 15, 21, 34, 26, 52, 78, 78, 52, 26, 34, 55, 45, 107, 207, 247, 207, 107, 45, 55, 89, 80, 218, 516, 784, 784, 516, 218, 80, 89, 144, 140, 442, 1288, 2349, 2905, 2349, 1288, 442, 140, 144, 233

Offset

1,2

Comments

Table starts

..1..2...3....5.....8.....13.....21......34.......55........89........144

..2..1...3....5.....8.....15.....26......45.......80.......140........245

..3..3...6...13....26.....52....107.....218......442.......899.......1829

..5..5..13...31....78....207....516....1288.....3270......8271......20866

..8..8..26...78...247....784...2349....7191....22268.....68384.....210050

.13.15..52..207...784...2905..10496...38721...144148....531780....1960675

.21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716

.34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113

.55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281

Links

R. H. Hardin, Table of n, a(n) for n = 1..924

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8

k=4: [order 13] for n>14

k=5: [order 23] for n>24

k=6: [order 37] for n>38

k=7: [order 63] for n>64

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A193147.

Sequence in context: A303719 A299595 A304270 * A071450 A175457 A322025

Adjacent sequences: A318542 A318543 A318544 * A318546 A318547 A318548

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 28 2018

Status

approved