A302953 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 86, 34, 0, 5, 161, 519, 587, 111, 0, 8, 601, 3626, 6531, 3815, 361, 0, 13, 2208, 26167, 87901, 80589, 25131, 1172, 0, 21, 8053, 185810, 1248691, 2104533, 998670, 164916, 3809, 0, 34, 29415, 1317541, 17374552, 58679318

Offset: 1

Author

R. H. Hardin, Apr 16 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0.....1.......1..........2............3...............5..................8

.0.....3......15.........46..........161.............601...............2208

.0....11......86........519.........3626...........26167.............185810

.0....34.....587.......6531........87901.........1248691...........17374552

.0...111....3815......80589......2104533........58679318.........1596912288

.0...361...25131.....998670.....50519822......2766909379.......147310312318

.0..1172..164916...12365841...1212025201....130376252119.....13578993819785

.0..3809.1083375..153141597..29081585941...6144174797769...1251888966185979

.0.12377.7114906.1896492042.697771332458.289545909430332.115412264434282781

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A232077(n-1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +15*a(n-2) +13*a(n-3) -2*a(n-4) -19*a(n-5) -3*a(n-6) +4*a(n-8)

k=4: [order 13]

k=5: [order 43] for n>44

Empirical for row n:

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

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

n=3: [order 7] for n>9

n=4: [order 24] for n>25

n=5: [order 73] for n>74