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A211556 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values 1

%I #4 Apr 15 2012 11:14:49

%S 180,1712,16318,155904,1492928,14327826,137797604,1327935624,

%T 12821402190,124011705656,1201438512040,11657189258802,

%U 113261149760588,1101805278189552,10730222804297534,104601472189182192

%N Number of (n+1)X(n+1) -9..9 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="/A211556/b211556.txt">Table of n, a(n) for n = 1..54</a>

%F Empirical: a(n) = 94*a(n-1) -3990*a(n-2) +100725*a(n-3) -1674425*a(n-4) +19135732*a(n-5) -151829733*a(n-6) +819081545*a(n-7) -2798053008*a(n-8) +4813088305*a(n-9) +909604521*a(n-10) -14434966072*a(n-11) -404287970*a(n-12) +26746796493*a(n-13) +30215600922*a(n-14) +16403931314*a(n-15) +5216836244*a(n-16) +1016849976*a(n-17) +119142480*a(n-18) +7668288*a(n-19) +207360*a(n-20)

%e Some solutions for n=3

%e ..8..0..6.-2...-8..5.-7..2....1.-1..0..3....5.-3..6..2....1.-1..4..2

%e ..0.-8..2.-6....5.-2..4..1...-1..1..0.-3...-3..1.-4.-4...-1..1.-4.-2

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

%e .-2.-6..0.-4....2..1..1..4....3.-3..4.-7....2.-4..1.-9....2.-2.-1.-5

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 15 2012

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