A298221 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 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, 40, 40, 73, 32, 64, 157, 89, 120, 89, 157, 64, 128, 353, 195, 503, 503, 195, 353, 128, 256, 869, 451, 1492, 2066, 1492, 451, 869, 256, 512, 1993, 1046, 4767, 6598, 6598, 4767, 1046, 1993, 512, 1024, 4557, 2453

Offset

1,2

Comments

Table starts

...1....2....4.....8.....16......32.......64.......128........256.........512

...2....7...13....29.....73.....157......353.......869.......1993........4557

...4...13...20....40.....89.....195......451......1046.......2453........5810

...8...29...40...120....503....1492.....4767.....17127......56292......185937

..16...73...89...503...2066....6598....30780....125759.....498466.....2153157

..32..157..195..1492...6598...25717...150617....749072....3768994....20393224

..64..353..451..4767..30780..150617..1261845...8555774...57269902...425814658

.128..869.1046.17127.125759..749072..8555774..72407248..624571738..6148262835

.256.1993.2453.56292.498466.3768994.57269902.624571738.7205019743.93491026869

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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 14] for n>15

k=4: [order 62] for n>65

Example

Some solutions for n=6 k=4
..0..0..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0
..1..1..0..0. .1..1..0..1. .1..0..1..0. .1..0..0..1. .1..0..1..1
..0..1..1..1. .0..0..0..0. .0..0..1..0. .0..0..1..0. .1..0..0..0
..0..1..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..0. .1..0..0..1
..1..0..1..1. .0..1..0..1. .1..0..1..1. .1..0..0..1. .0..1..1..0
..0..1..0..0. .0..0..0..1. .0..0..1..0. .0..1..0..1. .1..1..1..1

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A298494 A299187 A299948 * A299350 A299097 A299879

Adjacent sequences: A298218 A298219 A298220 * A298222 A298223 A298224

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2018

Status

approved