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A303808
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.
8
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 35, 15, 15, 35, 13, 21, 61, 27, 38, 27, 61, 21, 34, 127, 47, 55, 55, 47, 127, 34, 55, 265, 83, 107, 100, 107, 83, 265, 55, 89, 507, 161, 202, 174, 174, 202, 161, 507, 89, 144, 1013, 321, 438, 291, 316, 291, 438, 321, 1013
OFFSET
1,2
COMMENTS
Table starts
..1...2...3...5....8...13...21....34....55.....89....144.....233.....377
..2...5...7..17...35...61..127...265...507...1013...2071....4097....8147
..3...7...9..15...27...47...83...161...321....641...1293....2665....5603
..5..17..15..38...55..107..202...438...853...1858...3939....8667...18603
..8..35..27..55..100..174..291...588..1163...2423...4818...10036...21078
.13..61..47.107..174..316..597..1298..2799...6188..13927...32115...74576
.21.127..83.202..291..597.1217..2767..6147..14940..34846...84947..210191
.34.265.161.438..588.1298.2767..8004.19046..51822.132022..357534..963760
.55.507.321.853.1163.2799.6147.19046.52464.153020.411258.1212211.3473865
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) +4*a(n-3) -4*a(n-4) for n>5
k=3: [order 10]
k=4: [order 20] for n>24
k=5: [order 42] for n>46
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..1..0..1. .0..1..1..1
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1
..1..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
..1..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0
..1..1..1..1. .1..0..0..0. .0..0..0..1. .0..1..0..1. .1..0..0..0
CROSSREFS
Column 1 is A000045(n+1).
Sequence in context: A240406 A303682 A304133 * A304855 A304544 A306129
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 30 2018
STATUS
approved