A316448 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 57, 45, 3, 5, 120, 182, 182, 120, 5, 8, 333, 712, 946, 712, 333, 8, 13, 928, 2832, 5256, 5256, 2832, 928, 13, 21, 2613, 10696, 26592, 43568, 26592, 10696, 2613, 21, 34, 7400, 41107, 139705, 325839, 325839, 139705, 41107

Offset

1,5

Comments

Table starts

..0....1......1.......2.........3..........5............8............13

..1....7.....16......45.......120........333..........928..........2613

..1...16.....57.....182.......712.......2832........10696.........41107

..2...45....182.....946......5256......26592.......139705........743357

..3..120....712....5256.....43568.....325839......2520180......19750414

..5..333...2832...26592....325839....3624515.....39827783.....450251619

..8..928..10696..139705...2520180...39827783....621643922...10080547097

.13.2613..41107..743357..19750414..450251619..10080547097..235652502418

.21.7400.157988.3895564.153125421.5054524591.161747868059.5454074957154

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 69] for n>71

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A304959 A316641 A304697 * A316130 A317436 A303896

Adjacent sequences: A316445 A316446 A316447 * A316449 A316450 A316451

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 03 2018

Status

approved