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A302515
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 11, 6, 16, 13, 7, 15, 9, 9, 32, 21, 13, 21, 28, 14, 14, 64, 34, 23, 52, 36, 48, 21, 22, 128, 55, 37, 118, 80, 90, 89, 28, 35, 256, 89, 63, 220, 235, 199, 184, 163, 37, 56, 512, 144, 109, 408, 541, 689, 458, 376, 297, 51, 90, 1024, 233, 183
OFFSET
1,2
COMMENTS
Table starts
...1..2..3...5....8...13....21.....34......55......89......144.......233
...2..3..3...5....7...13....23.....37......63.....109......183.......309
...4..4.11..15...21...52...118....220.....408.....852.....1764......3460
...8..6..9..28...36...80...235....541....1115....2554.....6095.....13920
..16..9.14..48...90..199...689...2125....5410...13908....39850....114503
..32.14.21..89..184..458..1784...7182...22544...67096...220654....775150
..64.22.28.163..376.1088..4558..23944...95681..344525..1302832...5550086
.128.35.37.297..832.2651.12324..82857..414880.1775176..7735877..39371229
.256.56.51.544.1744.6257.32336.282857.1748514.8778929.44362463.272701915
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-4) for n>7
k=4: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) -a(n-6) -a(n-7) for n>10
k=5: a(n) = a(n-1) +6*a(n-3) +2*a(n-5) -12*a(n-6) -4*a(n-7) +8*a(n-9) for n>11
k=6: a(n) = a(n-1) +6*a(n-3) +5*a(n-4) +3*a(n-5) -8*a(n-6) -6*a(n-7) -3*a(n-8) for n>12
k=7: [order 15] for n>21
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +2*a(n-3) +4*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +5*a(n-4) -a(n-5) -5*a(n-6) -4*a(n-7) for n>10
n=5: [order 13] for n>17
n=6: [order 23] for n>29
n=7: [order 50] for n>55
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..1..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..0..1
..1..0..1..0. .0..0..1..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
..1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..0..0. .1..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003227(n-1) for n>2.
Sequence in context: A153928 A119446 A302680 * A303314 A349122 A076918
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 09 2018
STATUS
approved