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A297823
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 king-move adjacent elements, with upper left element zero.
8
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 399, 466, 399, 573, 8, 13, 1933, 1114, 1395, 1395, 1114, 1933, 13, 21, 6538, 3124, 4306, 4444, 4306, 3124, 6538, 21, 34, 22165, 8861, 13417, 14237, 14237, 13417, 8861, 22165, 34
OFFSET
1,5
COMMENTS
Table starts
..0.....1.....1......2......3.......5.......8.......13.......21........34
..1.....4....17.....49....166.....573....1933.....6538....22165.....75089
..1....17....48....146....399....1114....3124.....8861....25130.....71196
..2....49...146....466...1395....4306...13417....41512...128084....395130
..3...166...399...1395...4444...14237...43931...134395...412427...1268252
..5...573..1114...4306..14237...46701..146530...456814..1433279...4501076
..8..1933..3124..13417..43931..146530..467104..1485611..4742326..15121792
.13..6538..8861..41512.134395..456814.1485611..4833331.15742632..51146914
.21.22165.25130.128084.412427.1433279.4742326.15742632.52153064.172452330
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 9] for n>11
k=4: [order 18] for n>21
k=5: [order 49] for n>55
k=6: [order 98] for n>107
EXAMPLE
Some solutions for n=6 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..1..0
..1..0..0..1. .0..1..0..0. .0..1..0..0. .0..1..1..0. .1..0..0..1
..1..1..1..0. .1..1..0..1. .0..1..1..1. .1..0..0..1. .1..1..0..1
..0..0..0..1. .0..1..0..1. .1..0..0..0. .0..1..1..0. .0..1..0..1
..1..1..0..1. .0..1..0..1. .1..1..1..1. .1..0..0..1. .1..0..0..1
..1..1..0..1. .0..0..1..0. .0..0..0..1. .0..1..1..0. .1..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Sequence in context: A298570 A284771 A283042 * A297993 A298846 A298653
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 06 2018
STATUS
approved