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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A001519(n+1)

Column 2 is A004254(n+1)

Sequence in context: A063786 A121304 A002106 * A184604 A064630 A089793

Adjacent sequences: A232313 A232314 A232315 * A232317 A232318 A232319

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2013

Status

approved