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A302953
T(n,k) = Number of n X k 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
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
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 * A350464 A247706 A361527
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 16 2018
STATUS
approved