|
|
A304959
|
|
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
|
|
7
|
|
|
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 42, 45, 3, 5, 120, 118, 118, 120, 5, 8, 333, 371, 496, 371, 333, 8, 13, 928, 1203, 2080, 2080, 1203, 928, 13, 21, 2613, 3917, 8361, 11282, 8361, 3917, 2613, 21, 34, 7400, 12919, 35441, 60568, 60568, 35441, 12919, 7400, 34
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
Table starts
..0....1.....1......2........3.........5..........8..........13...........21
..1....7....16.....45......120.......333........928........2613.........7400
..1...16....42....118......371......1203.......3917.......12919........42060
..2...45...118....496.....2080......8361......35441......148491.......621640
..3..120...371...2080....11282.....60568.....334906.....1852576.....10208628
..5..333..1203...8361....60568....435964....3174054....23304518....170481467
..8..928..3917..35441...334906...3174054...30361694...294236689...2849022835
.13.2613.12919.148491..1852576..23304518..294236689..3805684538..49133027076
.21.7400.42060.621640.10208628.170481467.2849022835.49133027076.844100991906
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
k=3: [order 20] for n>21
k=4: [order 69] for n>71
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..0..1. .0..0..1..1. .0..0..1..1. .0..1..1..0. .0..0..0..1
..0..0..0..1. .1..0..0..1. .0..1..0..0. .1..1..0..0. .1..0..0..0
..1..1..0..1. .1..1..1..0. .0..1..1..0. .1..1..1..0. .0..0..0..1
..0..1..1..0. .1..0..1..0. .1..0..0..1. .1..0..1..0. .0..0..1..1
..0..0..0..0. .1..1..0..0. .1..0..1..1. .1..1..0..0. .1..0..1..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|