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A301330
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 10, 7, 10, 1, 1, 13, 18, 18, 13, 1, 1, 42, 25, 45, 25, 42, 1, 1, 74, 89, 143, 143, 89, 74, 1, 1, 188, 233, 414, 664, 414, 233, 188, 1, 1, 387, 552, 1481, 2520, 2520, 1481, 552, 387, 1, 1, 885, 1559, 5062, 12342, 17491, 12342, 5062, 1559, 885, 1, 1
OFFSET
1,5
COMMENTS
Table starts
.1...1....1.....1......1.......1........1..........1...........1............1
.1...3....2....10.....13......42.......74........188.........387..........885
.1...2....7....18.....25......89......233........552........1559.........4206
.1..10...18....45....143.....414.....1481.......5062.......17879........62112
.1..13...25...143....664....2520....12342......59524......283455......1368684
.1..42...89...414...2520...17491...116017.....770874.....5227338.....35859578
.1..74..233..1481..12342..116017..1127238...10358770....99285038....951443834
.1.188..552..5062..59524..770874.10358770..135428462..1814828567..24270760178
.1.387.1559.17879.283455.5227338.99285038.1814828567.34057380439.641360375141
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 4*a(n-2) +2*a(n-3) +a(n-5) -3*a(n-6) +a(n-7)
k=3: [order 28] for n>29
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..0..0..0. .1..1..0..0. .0..1..0..1
..0..1..0..0. .1..0..1..0. .1..1..1..1. .0..0..1..0. .0..0..1..1
..0..0..1..0. .1..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..0
..1..0..0..1. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..0..0
CROSSREFS
Column 2 is A300374.
Sequence in context: A300380 A300682 A300605 * A175636 A352935 A364757
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 18 2018
STATUS
approved