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A305047
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.
8
1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 17, 20, 20, 17, 99, 1, 1, 194, 40, 17, 55, 17, 40, 194, 1, 1, 387, 73, 25, 201, 201, 25, 73, 387, 1, 1, 773, 87, 70, 337, 137, 337, 70, 87, 773, 1, 1, 1538, 219, 67, 1359, 42, 42, 1359
OFFSET
1,5
COMMENTS
Table starts
.1...1..1..1....1....1....1.......1.......1.......1.........1..........1
.1...4..7.13...26...49...99.....194.....387.....773......1538.......3081
.1...7..5..9...15...17...40......73......87.....219.......433........583
.1..13..9.11...20...17...25......70......67.....101.......292........325
.1..26.15.20...55..201..337....1359....5918...13840.....50917.....214418
.1..49.17.17..201..137...42....5165....6357....5846....188507.....395242
.1..99.40.25..337...42..116....6542....3137....4862....144931.....173351
.1.194.73.70.1359.5165.6542..273937.1450263.3623207..71239378..487361093
.1.387.87.67.5918.6357.3137.1450263.2062731.1912261.381186998.1094057409
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 11] for n>13
k=4: [order 9] for n>13
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..1
..1..1..0..0. .1..1..1..1. .1..1..0..1. .0..1..1..0. .0..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..0. .0..0..0..1
..0..1..0..0. .1..1..1..1. .1..1..0..0. .0..1..1..0. .0..0..0..1
..1..0..1..1. .1..1..1..1. .1..1..0..1. .0..1..1..0. .0..0..0..1
CROSSREFS
Column 2 is A304004.
Sequence in context: A081577 A146986 A304141 * A316733 A304010 A305360
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 24 2018
STATUS
approved