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A297506
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.
13
1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914
OFFSET
1,2
COMMENTS
Table starts
.1.....2.......4........7.........12...........21.............37
.1....10......31.......68........218..........729...........2097
.1....29.....110......314.......1829.........8803..........34757
.1....87.....531.....2281......23348.......191192........1247716
.1...280....2534....14201.....270845......3624914.......35049871
.1...876...11405....88808....3075264.....66289769......978288822
.1..2735...53175...573119...35919085...1272836591....28914051279
.1..8583..246040..3613793..414559944..23896899569...823340493402
.1.26900.1135117.22999331.4794512057.450529429259.23748019543354
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
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 11]
k=4: [order 18]
k=5: [order 50]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)
n=3: [order 10]
n=4: [order 24]
n=5: [order 59]
EXAMPLE
Some solutions for n=4 k=4
..1..1..1..1. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..1. .0..1..0..0. .0..0..0..0
..1..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..1. .0..0..0..1
..1..1..0..0. .1..1..0..0. .1..1..0..0. .0..1..1..0. .0..0..1..1
CROSSREFS
Column 2 is A295525.
Row 1 is A005251(n+2).
Sequence in context: A137634 A100229 A071949 * A297720 A297654 A220922
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 31 2017
STATUS
approved