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A211257
Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values
1
85, 231, 547, 1283, 2901, 6595, 14775, 33409, 75157, 170723, 387687, 888293, 2039449, 4718583, 10949039, 25566565, 59877913, 140930679, 332585711, 787830185, 1870341077, 4452666039, 10618825855, 25375634725, 60720707925
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) = 6*a(n-1) +6*a(n-2) -97*a(n-3) +62*a(n-4) +668*a(n-5) -852*a(n-6) -2556*a(n-7) +4359*a(n-8) +5935*a(n-9) -12593*a(n-10) -8545*a(n-11) +22727*a(n-12) +7400*a(n-13) -26431*a(n-14) -3396*a(n-15) +19783*a(n-16) +389*a(n-17) -9298*a(n-18) +302*a(n-19) +2606*a(n-20) -118*a(n-21) -392*a(n-22) +12*a(n-23) +24*a(n-24)
EXAMPLE
Some solutions for n=3
..3.-2..1.-2...-4..2.-2..1....4..0..0..0...-2..1.-1..2....3.-1..2.-1
.-2..1..0..1....2..0..0..1....0.-4..4.-4....1..0..0.-1...-1.-1..0.-1
..1..0.-1..0...-2..0..0.-1....0..4.-4..4...-1..0..0..1....2..0..1..0
.-2..1..0..1....1..1.-1..2....0.-4..4.-4....2.-1..1.-2...-1.-1..0.-1
CROSSREFS
Sequence in context: A044798 A260100 A072289 * A027524 A043340 A045129
KEYWORD
nonn
AUTHOR
R. H. Hardin Apr 06 2012
STATUS
approved