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A302953 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 86, 34, 0, 5, 161, 519, 587, 111, 0, 8, 601, 3626, 6531, 3815, 361, 0, 13, 2208, 26167, 87901, 80589, 25131, 1172, 0, 21, 8053, 185810, 1248691, 2104533, 998670, 164916, 3809, 0, 34, 29415, 1317541, 17374552, 58679318 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

.0.....3......15.........46..........161.............601...............2208

.0....11......86........519.........3626...........26167.............185810

.0....34.....587.......6531........87901.........1248691...........17374552

.0...111....3815......80589......2104533........58679318.........1596912288

.0...361...25131.....998670.....50519822......2766909379.......147310312318

.0..1172..164916...12365841...1212025201....130376252119.....13578993819785

.0..3809.1083375..153141597..29081585941...6144174797769...1251888966185979

.0.12377.7114906.1896492042.697771332458.289545909430332.115412264434282781

LINKS

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

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +15*a(n-2) +13*a(n-3) -2*a(n-4) -19*a(n-5) -3*a(n-6) +4*a(n-8)

k=4: [order 13]

k=5: [order 43] for n>44

Empirical for row n:

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

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

n=3: [order 7] for n>9

n=4: [order 24] for n>25

n=5: [order 73] for n>74

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..0. .0..0..0..1

..1..0..0..0. .0..0..0..1. .1..0..1..0. .1..0..1..1. .0..0..1..1

..1..0..0..0. .1..1..1..0. .0..0..0..1. .0..0..1..0. .1..1..0..1

..0..1..1..0. .1..1..0..1. .1..1..1..0. .0..0..0..0. .1..0..1..1

..1..1..0..1. .0..0..1..1. .0..0..1..1. .0..1..1..0. .0..0..0..0

CROSSREFS

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A232077(n-1).

Sequence in context: A256068 A302381 A303102 * A247706 A247704 A127802

Adjacent sequences:  A302950 A302951 A302952 * A302954 A302955 A302956

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 16 2018

STATUS

approved

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Last modified May 7 08:32 EDT 2021. Contains 343636 sequences. (Running on oeis4.)