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R. H. Hardin, <a href="/A211713/b211713.txt">Table of n, a(n) for n = 1..201</a>

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Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

264, 726, 1670, 3574, 7448, 15136, 30436, 60938, 120832, 241150, 476020, 951586, 1878928, 3771022, 7467440, 15063942, 29958046, 60772582, 121463624, 247803532, 497864910, 1021347926, 2062591634, 4253485786, 8631871242, 17886996814

1,1

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)

Empirical: a(n) = 5*a(n-1) +23*a(n-2) -149*a(n-3) -196*a(n-4) +2007*a(n-5) +424*a(n-6) -16175*a(n-7) +5683*a(n-8) +87013*a(n-9) -61030*a(n-10) -330011*a(n-11) +313597*a(n-12) +908524*a(n-13) -1043207*a(n-14) -1841180*a(n-15) +2438675*a(n-16) +2754829*a(n-17) -4138459*a(n-18) -3021301*a(n-19) +5162035*a(n-20) +2381895*a(n-21) -4737637*a(n-22) -1297351*a(n-23) +3176171*a(n-24) +447161*a(n-25) -1532186*a(n-26) -72331*a(n-27) +519056*a(n-28) -8146*a(n-29) -118840*a(n-30) +6266*a(n-31) +17252*a(n-32) -1128*a(n-33) -1408*a(n-34) +72*a(n-35) +48*a(n-36)

Some solutions for n=3

.-3..0..0..6...-7..4.-1..4..-11..1.-5..1....6.-8..6.-8....2..2..2.-3

..0..3.-3.-3....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10....2.-6..2.-1

..0.-3..3..3...-1.-2..5.-2...-5.-5..1.-5....6.-8..6.-8....2..2..2.-3

..6.-3..3.-9....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10...-3.-1.-3..4

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R. H. Hardin Apr 20 2012

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