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A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s. 8
1, 2, 2, 4, 10, 4, 7, 29, 29, 7, 12, 87, 147, 87, 12, 21, 280, 774, 774, 280, 21, 37, 876, 4080, 7071, 4080, 876, 37, 65, 2735, 21489, 64189, 64189, 21489, 2735, 65, 114, 8583, 113466, 588529, 1012315, 588529, 113466, 8583, 114, 200, 26900, 598374, 5400933 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4.........7..........12............21...............37
...2....10......29........87.........280...........876.............2735
...4....29.....147.......774........4080.........21489...........113466
...7....87.....774......7071.......64189........588529..........5400933
..12...280....4080.....64189.....1012315......16031147........253594307
..21...876...21489....588529....16031147.....437241277......11938414614
..37..2735..113466...5400933...253594307...11938414614.....563330031268
..65..8583..598374..49414072..4003959566..325438086413...26515589323171
.114.26900.3155426.452274232.63279327977.8875686431050.1248681784524804
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 18]
k=4: [order 45]
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .0..1..1..0
..0..1..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..0
..1..1..0..0. .0..1..1..0. .1..0..0..1. .1..1..0..1. .1..1..0..0
..0..0..1..1. .1..1..1..0. .1..0..0..0. .1..0..0..1. .0..1..0..1
..0..0..1..1. .1..1..0..0. .0..1..1..0. .1..1..1..0. .0..1..1..1
CROSSREFS
Column 1 is A005251(n+2).
Sequence in context: A296386 A296643 A295040 * A220259 A220323 A295416
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 23 2017
STATUS
approved

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Last modified March 2 15:53 EST 2024. Contains 370494 sequences. (Running on oeis4.)