A299879 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 41, 41, 73, 32, 64, 157, 102, 125, 102, 157, 64, 128, 353, 253, 585, 585, 253, 353, 128, 256, 869, 632, 1974, 3068, 1974, 632, 869, 256, 512, 1993, 1563, 6542, 11263, 11263, 6542, 1563, 1993, 512, 1024, 4557

Offset

1,2

Comments

Table starts

...1....2....4.....8......16.......32........64........128.........256

...2....7...13....29......73......157.......353........869........1993

...4...13...20....41.....102......253.......632.......1563........3896

...8...29...41...125.....585.....1974......6542......24545.......89192

..16...73..102...585....3068....11263.....53159.....246537.....1098723

..32..157..253..1974...11263....54005....324797....1859944....10716128

..64..353..632..6542...53159...324797...2714797...21236116...164681059

.128..869.1563.24545..246537..1859944..21236116..213883244..2166043717

.256.1993.3896.89192.1098723.10716128.164681059.2166043717.29310012663

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) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6

k=3: [order 16] for n>17

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A298221 A299350 A299097 * A299015 A299806 A299682

Adjacent sequences: A299876 A299877 A299878 * A299880 A299881 A299882

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 21 2018

Status

approved