A211473 - OEIS

%I #4 Apr 12 2012 06:38:49

%S 144,1224,10416,88776,757784,6478064,55460120,475479800,4082006352,

%T 35089391112,301998774840,2602109942640,22443946490552,

%U 193770109394072,1674359497311056,14479231995139496,125296349390355480

%N Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

%C 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)

%H R. H. Hardin, <a href="/A211473/b211473.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical: a(n) = 75*a(n-1) -2510*a(n-2) +49200*a(n-3) -622175*a(n-4) +5253075*a(n-5) -29416155*a(n-6) +102987225*a(n-7) -184111448*a(n-8) -476940*a(n-9) +472118829*a(n-10) -56520825*a(n-11) -794496080*a(n-12) -750911850*a(n-13) -339742508*a(n-14) -86830200*a(n-15) -12751696*a(n-16) -999360*a(n-17) -32256*a(n-18)

%e Some solutions for n=3

%e .-6..3..1..1....5.-6..3.-2...-8..4.-7..4...-5..3..1..3...-1.-2..1.-3

%e ..3..0.-4..2...-6..7.-4..3....4..0..3..0....3.-1.-3.-1...-2..5.-4..6

%e ..1.-4..8.-6....3.-4..1..0...-7..3.-6..3....1.-3..7.-3....1.-4..3.-5

%e ..1..2.-6..4...-2..3..0.-1....4..0..3..0....3.-1.-3.-1...-3..6.-5..7

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 12 2012