login
A211255
Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values
1
65, 143, 287, 567, 1109, 2145, 4163, 8041, 15609, 30271, 58955, 114925, 224757, 440281, 864529, 1700629, 3351109, 6614459, 13071953, 25871279, 51248961, 101644005, 201725287, 400751925, 796518335, 1584431751, 3152835011
OFFSET
1,1
COMMENTS
Symmetry and 2X2 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) +5*a(n-2) -36*a(n-3) +5*a(n-4) +123*a(n-5) -69*a(n-6) -205*a(n-7) +150*a(n-8) +176*a(n-9) -138*a(n-10) -74*a(n-11) +56*a(n-12) +12*a(n-13) -8*a(n-14)
EXAMPLE
Some solutions for n=3
..4.-3..4.-5....4.-2..4.-2....1..0.-1.-3....2.-1..0..1...-6..4.-2..0
.-3..2.-3..4...-2..0.-2..0....0.-1..2..2...-1..0..1.-2....4.-2..0..2
..4.-3..4.-5....4.-2..4.-2...-1..2.-3.-1....0..1.-2..3...-2..0..2.-4
.-5..4.-5..6...-2..0.-2..0...-3..2.-1..5....1.-2..3.-4....0..2.-4..6
CROSSREFS
Sequence in context: A285300 A194002 A092226 * A297849 A226926 A345700
KEYWORD
nonn
AUTHOR
R. H. Hardin Apr 06 2012
STATUS
approved