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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 05:37 EDT 2020. Contains 336197 sequences. (Running on oeis4.)