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A300146 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 1, 16, 0, 1, 48, 18, 18, 48, 1, 0, 88, 41, 246, 41, 88, 0, 1, 240, 130, 1043, 1043, 130, 240, 1, 0, 704, 510, 5368, 13182, 5368, 510, 704, 0, 1, 1600, 1740, 37739, 78147, 78147, 37739, 1740, 1600, 1, 0, 4032, 5554, 219689, 913701 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.0....1....0.......1........0..........1............0..............1
.1....4....4......16.......48.........88..........240............704
.0....4....1......18.......41........130..........510...........1740
.1...16...18.....246.....1043.......5368........37739.........219689
.0...48...41....1043....13182......78147.......913701.......11122233
.1...88..130....5368....78147....1048462.....21602016......399714825
.0..240..510...37739...913701...21602016....783899343....25183985328
.1..704.1740..219689.11122233..399714825..25183985328..1507189100633
.0.1600.5554.1245482.99027295.6588098950.731705422933.74614900420199
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)
k=3: [order 15] for n>17
k=4: [order 40] for n>42
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..1. .1..0..1..1
..0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..1..0..0
..0..0..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0. .1..0..0..0
CROSSREFS
Column 2 is A298448.
Sequence in context: A298834 A299588 A299528 * A100045 A143844 A186759
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 26 2018
STATUS
approved

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Last modified June 18 14:18 EDT 2024. Contains 373481 sequences. (Running on oeis4.)