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A296725
T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.
8
2, 3, 3, 5, 9, 5, 8, 21, 21, 8, 13, 57, 69, 57, 13, 21, 153, 258, 258, 153, 21, 34, 393, 963, 1463, 963, 393, 34, 55, 1041, 3493, 8315, 8315, 3493, 1041, 55, 89, 2745, 12860, 44668, 72533, 44668, 12860, 2745, 89, 144, 7185, 47305, 246923, 579857, 579857, 246923
OFFSET
1,1
COMMENTS
Table starts
..2....3......5.......8........13..........21...........34.............55
..3....9.....21......57.......153.........393.........1041...........2745
..5...21.....69.....258.......963........3493........12860..........47305
..8...57....258....1463......8315.......44668.......246923........1364492
.13..153....963....8315.....72533......579857......4846823.......40521141
.21..393...3493...44668....579857.....6829945.....84312938.....1042553987
.34.1041..12860..246923...4846823....84312938...1554755519....28740762011
.55.2745..47305.1364492..40521141..1042553987..28740762011...795154816254
.89.7185.173498.7488185.334815607.12735280455.523224064059.21598350633016
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +2*a(n-2) +6*a(n-3)
k=3: [order 10]
k=4: [order 18]
k=5: [order 45]
EXAMPLE
Some solutions for n=5 k=4
..1..0..0..0. .1..0..0..1. .0..0..0..0. .1..0..1..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..0
..0..0..1..0. .0..0..1..0. .1..1..0..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1. .0..1..0..0
..1..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
CROSSREFS
Column 1 is A000045(n+2).
Sequence in context: A317644 A194000 A295781 * A296588 A065460 A241741
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 19 2017
STATUS
approved