A302635 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 8, 10, 16, 13, 25, 14, 19, 21, 32, 21, 65, 25, 33, 42, 42, 64, 34, 185, 47, 65, 101, 82, 86, 128, 55, 385, 83, 149, 257, 248, 189, 179, 256, 89, 649, 150, 304, 691, 719, 657, 469, 370, 512, 144, 1489, 269, 643, 1734, 2262, 2303, 1841, 1029

Offset: 1

Author

R. H. Hardin, Apr 10 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

...2...3....9...17....25.....65....185.....385......649.....1489......3929

...4...6....8...14....25.....47.....83.....150......269......488.......876

...8..10...19...33....65....149....304.....643.....1343.....2880......6038

..16..21...42..101...257....691...1734....4502....11524....30121.....77399

..32..42...82..248...719...2262...6460...19799....59002...179668....535412

..64..86..189..657..2303...8981..30216..112431...408512..1512824...5441957

.128.179..469.1841..7695..35772.144266..652931..2863575.12800635..55765517

.256.370.1029.4892.24205.135125.642553.3499587.18446157.98898783.515558643

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..391

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513.

Row 1 is A000045(n+1).

Row 2 is A302164.

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13

k=4: [order 21] for n>25

k=5: [order 29] for n>32

k=6: [order 54] for n>65

Empirical for row n:

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

n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

n=3: a(n) = a(n-1) +a(n-2) +2*a(n-4) -a(n-5) for n>7

n=4: [order 22] for n>23

n=5: [order 63] for n>64

n=6: [order 81] for n>86