|
|
A211115
|
|
Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two or three distinct values.
|
|
1
|
|
|
12, 26, 54, 106, 208, 398, 766, 1458, 2792, 5324, 10206, 19550, 37616, 72446, 140048, 271194, 526792, 1025268, 2000636, 3911284, 7663264, 15040266, 29571962, 58231566, 114837690, 226761020, 448318274, 887305854, 1757921506, 3485905204
(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) = 5*a(n-1) - 4*a(n-2) - 16*a(n-3) + 27*a(n-4) + 8*a(n-5) - 35*a(n-6) + 10*a(n-7) + 10*a(n-8) - 4*a(n-9).
Empirical g.f.: 2*x*(6 - 17*x - 14*x^2 + 66*x^3 - 7*x^4 - 76*x^5 + 29*x^6 + 22*x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 15 2018
|
|
EXAMPLE
|
Some solutions for n=3:
..0.-1..0.-1...-2..0.-1..0....1.-1..0.-1....2..0..0.-2....2..0..1..0
.-1..2.-1..2....0..2.-1..2...-1..1..0..1....0.-2..2..0....0.-2..1.-2
..0.-1..0.-1...-1.-1..0.-1....0..0.-1..0....0..2.-2..0....1..1..0..1
.-1..2.-1..2....0..2.-1..2...-1..1..0..1...-2..0..0..2....0.-2..1.-2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|