A302820 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 75, 81, 16, 32, 136, 220, 389, 264, 32, 64, 360, 731, 1494, 1852, 857, 64, 128, 960, 2419, 6905, 9050, 8485, 2785, 128, 256, 2576, 7900, 34957, 57684, 51476, 41247, 9050, 256, 512, 6944, 25645, 170262, 455224, 454733

Offset

1,2

Comments

Table starts

...1.....2......4........8........16..........32...........64............128

...2.....8.....20.......52.......136.........360..........960...........2576

...4....25.....75......220.......731........2419.........7900..........25645

...8....81....389.....1494......6905.......34957.......170262.........800847

..16...264...1852.....9050.....57684......455224......3252934.......21373833

..32...857...8485....51476....454733.....5520999.....58122740......535479917

..64..2785..41247...317216...3825201....72576189...1135257814....14619284475

.128..9050.196946..1927184..32123578...960564532..22294687742...402121386052

.256.29407.931243.11448173.264639685.12417289008.427140472935.10807066934912

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 14]

k=4: [order 49] for n>51

Empirical for row n:

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

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

n=3: [order 15] for n>16

n=4: [order 67] for n>68

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Row 2 is A302323.

Sequence in context: A303182 A302322 A303016 * A303513 A303727 A305230

Adjacent sequences: A302817 A302818 A302819 * A302821 A302822 A302823

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 13 2018

Status

approved