login
A305367
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 39, 45, 3, 5, 120, 107, 107, 120, 5, 8, 333, 310, 398, 310, 333, 8, 13, 928, 943, 1532, 1532, 943, 928, 13, 21, 2613, 2935, 5465, 7196, 5465, 2935, 2613, 21, 34, 7400, 9077, 21691, 32765, 32765, 21691, 9077, 7400, 34, 55, 21053
OFFSET
1,5
COMMENTS
Table starts
..0....1.....1......2.......3........5.........8.........13..........21
..1....7....16.....45.....120......333.......928.......2613........7400
..1...16....39....107.....310......943......2935.......9077.......28054
..2...45...107....398....1532.....5465.....21691......82625......320130
..3..120...310...1532....7196....32765....163682.....791180.....3881007
..5..333...943...5465...32765...179644...1113793....6595796....39677540
..8..928..2935..21691..163682..1113793...8803975...65762626...500606134
.13.2613..9077..82625..791180..6595796..65762626..615439372..5858512208
.21.7400.28054.320130.3881007.39677540.500606134.5858512208.69977566829
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
k=3: [order 18]
k=4: [order 66] for n>68
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..1. .0..1..1..1
..1..0..1..0. .1..1..1..1. .1..0..1..0. .0..1..0..1. .1..1..1..0
..1..0..1..1. .1..0..0..1. .1..1..0..1. .1..1..1..0. .1..1..1..1
..1..0..0..1. .1..0..0..1. .0..1..1..0. .1..1..0..1. .0..0..1..0
..1..1..0..1. .1..0..0..1. .1..1..1..0. .0..0..1..0. .1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A304013.
Sequence in context: A305089 A316740 A304019 * A304959 A316641 A304697
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 31 2018
STATUS
approved