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A211719
Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero.
1
265, 3059, 35377, 409883, 4757545, 55318979, 644340577, 7517728043, 87854788825, 1028320041299, 12054528824977, 141515917523003, 1663668298132105, 19584269744002019, 230833988758608577, 2724058135239730763
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) = 23*a(n-1) - 132*a(n-2).
Conjectures from Colin Barker, Jul 19 2018: (Start)
G.f.: x*(265 - 3036*x) / ((1 - 11*x)*(1 - 12*x)).
a(n) = 11^(1+n) + 12^(1+n).
(End)
EXAMPLE
Some solutions for n=3.
..4..0.-3..1...-1..0..5.-5...-5.-1..3..6...11.-3.10.-9..-10..4.-7..0
..0.-4..7.-5....0..1.-6..6...-1..7.-9..0...-3.-5.-2..1....4..2..1..6
.-3..7-10..8....5.-6.11-11....3.-9.11.-2...10.-2..9.-8...-7..1.-4.-3
..1.-5..8.-6...-5..6-11.11....6..0.-2.-7...-9..1.-8..7....0..6.-3.10
CROSSREFS
Sequence in context: A183247 A094795 A023043 * A210120 A266308 A278141
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 20 2012
STATUS
approved