|
|
A211116
|
|
Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values.
|
|
1
|
|
|
13, 31, 75, 177, 415, 963, 2227, 5137, 11855, 27397, 63483, 147557, 344175, 805635, 1892433, 4460137, 10544415, 24999069, 59419405, 141550383, 337872559, 807871799, 1934541399, 4638401749, 11133523165, 26748531157, 64314484855
(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) = 7*a(n-1) - 15*a(n-2) + a(n-3) + 33*a(n-4) - 28*a(n-5) - 12*a(n-6) + 16*a(n-7) + a(n-8) - 2*a(n-9).
Empirical g.f.: x*(13 - 60*x + 53*x^2 + 104*x^3 - 159*x^4 - 21*x^5 + 83*x^6 + x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 16 2018
|
|
EXAMPLE
|
Some solutions for n=3:
..2..0..1.-2...-2..0.-2..0....2.-1..2.-1....0.-1.-1..0....2..0..2.-1
..0.-2..1..0....0..2..0..2...-1..0.-1..0...-1..2..0..1....0.-2..0.-1
..1..1..0.-1...-2..0.-2..0....2.-1..2.-1...-1..0.-2..1....2..0..2.-1
.-2..0.-1..2....0..2..0..2...-1..0.-1..0....0..1..1..0...-1.-1.-1..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|