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A304355 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero. 8
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 27, 27, 57, 13, 21, 125, 60, 101, 60, 125, 21, 34, 289, 123, 333, 333, 123, 289, 34, 55, 741, 280, 1023, 1540, 1023, 280, 741, 55, 89, 1737, 729, 4370, 5153, 5153, 4370, 729, 1737, 89, 144, 4045, 2015, 19555, 34887 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1....2....3.....5.......8.......13.........21...........34............55
..2....5....9....21......57......125........289..........741..........1737
..3....9...13....27......60......123........280..........729..........2015
..5...21...27...101.....333.....1023.......4370........19555.........81921
..8...57...60...333....1540.....5153......34887.......269948.......1656222
.13..125..123..1023....5153....36201.....445745......4761156......49676930
.21..289..280..4370...34887...445745....9176798....160397426....2593742186
.34..741..729.19555..269948..4761156..160397426...4663483164..115363289438
.55.1737.2015.81921.1656222.49676930.2593742186.115363289438.4502196415629
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)
k=3: [order 18] for n>20
k=4: [order 66] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..0..0..0
..1..0..0..1. .1..1..1..1. .1..1..1..1. .0..0..0..1. .1..0..0..1
..1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..0..1..0. .1..1..0..1. .0..1..1..0. .0..1..0..0. .0..1..0..0
CROSSREFS
Column 1 is A000045(n+1).
Sequence in context: A304931 A304669 A306172 * A305918 A305649 A316925
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 11 2018
STATUS
approved

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Last modified May 23 15:34 EDT 2024. Contains 372763 sequences. (Running on oeis4.)