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R. H. Hardin, <a href="/A211336/b211336.txt">Table of n, a(n) for n = 1..74</a>

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Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

60, 332, 1846, 10332, 58164, 329130, 1870664, 10670876, 61044918, 349974788, 2009495068, 11549465226, 66414142512, 381959562756, 2196335839046, 12624063953180, 72516570941316, 416247502883594, 2387248114517560

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) = 32*a(n-1) -429*a(n-2) +3078*a(n-3) -12340*a(n-4) +24890*a(n-5) -10895*a(n-6) -35870*a(n-7) +19131*a(n-8) +40338*a(n-9) +18694*a(n-10) +3532*a(n-11) +240*a(n-12)

Some solutions for n=3

.-3..1.-1..2....5.-3..0.-4....5.-2..4.-5....2..0.-1.-2....2.-1.-1..1

..1..1.-1..0...-3..1..2..2...-2.-1.-1..2....0.-2..3..0...-1..0..2.-2

.-1.-1..1..0....0..2.-5..1....4.-1..3.-4...-1..3.-4..1...-1..2.-4..4

..2..0..0.-1...-4..2..1..3...-5..2.-4..5...-2..0..1..2....1.-2..4.-4

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R. H. Hardin Apr 07 2012

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