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 A211551 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values 1

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

%S 151,347,697,1351,2573,4843,9101,17119,32217,61049,115711,221303,

%T 423135,816445,1574315,3060679,5945293,11628771,22724533,44657457,

%U 87680827,172920419,340748827,673800359,1331438461,2638045435,5223798103

%N Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and one or three 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="/A211551/b211551.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +11*a(n-2) -60*a(n-3) -34*a(n-4) +375*a(n-5) -53*a(n-6) -1270*a(n-7) +601*a(n-8) +2541*a(n-9) -1636*a(n-10) -3075*a(n-11) +2204*a(n-12) +2210*a(n-13) -1562*a(n-14) -875*a(n-15) +530*a(n-16) +150*a(n-17) -60*a(n-18)

%e Some solutions for n=3

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

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

%e ..8.-2..8.-3...-1.-1.-7.-1....5.-1..5.-2....4.-1..9.-1....3.-5..3.-5

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 15 2012

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Last modified June 17 23:25 EDT 2024. Contains 373468 sequences. (Running on oeis4.)