|
|
A211323
|
|
Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.
|
|
1
|
|
|
14, 24, 42, 76, 140, 262, 496, 948, 1826, 3540, 6900, 13510, 26552, 52348, 103474, 204972, 406748, 808326, 1608288, 3203044, 6384194, 12732964, 25408612, 50724486, 101298920, 202355052, 404317266, 807998908, 1614969356, 3228274630
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Symmetry and 2 X 2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j) = (x(i,i)+x(j,j))/2*(-1)^(i-j).
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
Empirical g.f.: 2*x*(7 - 16*x + x^2 + 9*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Jul 16 2018
|
|
EXAMPLE
|
Some solutions for n=3.
..3..0..3..0....2.-1..0.-2....0.-1.-1..0....1.-2..1.-2....2.-1..0.-1
..0.-3..0.-3...-1..0..1..1...-1..2..0..1...-2..3.-2..3...-1..0..1..0
..3..0..3..0....0..1.-2..0...-1..0.-2..1....1.-2..1.-2....0..1.-2..1
..0.-3..0.-3...-2..1..0..2....0..1..1..0...-2..3.-2..3...-1..0..1..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|