A232316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero.

2, 5, 5, 16, 24, 13, 52, 139, 115, 34, 169, 853, 1202, 551, 89, 549, 5241, 14042, 10409, 2640, 233, 1784, 32089, 164014, 231454, 90157, 12649, 610, 5797, 196698, 1905436, 5142441, 3815483, 780922, 60605, 1597, 18837, 1205422, 22161823, 113293694

Offset: 1

Author

R. H. Hardin, Nov 22 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....2.......5.........16............52..............169.................549

.....5......24........139...........853.............5241...............32089

....13.....115.......1202.........14042...........164014.............1905436

....34.....551......10409........231454..........5142441...........113293694

....89....2640......90157.......3815483........161243887..........6736602042

...233...12649.....780922......62897985.......5055954492........400571676322

...610...60605....6764246....1036869496.....158534446141......23818815015639

..1597..290376...58591124...17092731689....4971005036586....1416315842358249

..4181.1391275..507509767..281772661177..155870804492221...84217060496525106

.10946.6665999.4395993154.4645005493684.4887484036570530.5007720081104988709

Examples

			Some.solutions.for.n=3.k=4
..0..0..0..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..0
..0..0..1..1..1....0..1..1..0..0....0..0..0..1..1....0..1..1..0..1
..1..1..0..0..0....1..0..0..1..1....0..0..1..1..1....0..0..0..1..0
..1..1..1..1..1....1..1..1..0..0....0..0..0..0..0....1..1..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..390

Crossrefs

Column 1 is A001519(n+1)

Column 2 is A004254(n+1)

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) -11*a(n-2) -5*a(n-3) -a(n-4)

k=4: a(n) = 19*a(n-1) -44*a(n-2) +43*a(n-3) -19*a(n-4) +4*a(n-5) -2*a(n-6) for n>7

k=5: [order 12] for n>13

k=6: [order 18] for n>20

k=7: [order 37] for n>40

Empirical for row n:

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

n=2: [order 12] for n>14

n=3: [order 32] for n>34

n=4: [order 78] for n>82