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A318098 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 5, 1, 2, 16, 16, 2, 3, 50, 45, 50, 3, 5, 160, 220, 220, 160, 5, 8, 511, 795, 1563, 795, 511, 8, 13, 1634, 3310, 9193, 9193, 3310, 1634, 13, 21, 5226, 12774, 57744, 73788, 57744, 12774, 5226, 21, 34, 16716, 51298, 356786, 679923, 679923, 356786, 51298 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1......1........2.........3...........5............8.............13
..1.....5.....16.......50.......160.........511.........1634...........5226
..1....16.....45......220.......795........3310........12774..........51298
..2....50....220.....1563......9193.......57744.......356786........2215533
..3...160....795.....9193.....73788......679923......5965933.......53097417
..5...511...3310....57744....679923.....8985801....114914085.....1478603982
..8..1634..12774...356786...5965933...114914085...2154127036....40412593332
.13..5226..51298..2215533..53097417..1478603982..40412593332..1097965368750
.21.16716.201637.13752047.470312224.19018066407.760353849044.29957208854824
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) -3*a(n-4) -2*a(n-5) -a(n-6)
k=3: [order 19] for n>21
k=4: [order 72] for n>73
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
..1..1..1..1. .1..1..0..0. .1..0..1..1. .1..1..1..1. .1..1..1..1
..0..1..1..1. .0..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..0..1
..0..0..0..0. .0..0..1..1. .1..0..1..1. .1..0..0..0. .0..1..0..1
..1..0..0..1. .1..0..1..0. .1..0..0..0. .1..0..0..1. .1..1..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A317817.
Sequence in context: A197080 A317823 A318430 * A318068 A165449 A019114
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 16 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)