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%I #4 Apr 06 2012 11:02:12
%S 65,335,1703,8645,43643,219333,1097247,5465297,27114351,134027929,
%T 660336579,3243840829,15893481911,77692754369,379020868055,
%U 1845782118641,8974924575259,43581782793301,211388981838455,1024316233634281
%N Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one, 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="/A211259/b211259.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 28*a(n-1) -155*a(n-2) -2658*a(n-3) +32061*a(n-4) +66366*a(n-5) -2314922*a(n-6) +3159336*a(n-7) +97801748*a(n-8) -317172988*a(n-9) -2797365748*a(n-10) +13347627288*a(n-11) +57922813108*a(n-12) -369288318800*a(n-13) -900259137962*a(n-14) +7525220569156*a(n-15) +10736644664141*a(n-16) -118794611594160*a(n-17) -100177501866905*a(n-18) +1492188101583602*a(n-19) +756635414359131*a(n-20) -15127411602979766*a(n-21) -4996517564711412*a(n-22) +124488915629652484*a(n-23) +32496342097994312*a(n-24) -830961220175609104*a(n-25) -217952927487180360*a(n-26) +4471006873093739800*a(n-27) +1356224545195754860*a(n-28) -19189501086495681880*a(n-29) -6829521421681422792*a(n-30) +64885315804531962064*a(n-31) +25455961312177735008*a(n-32) -171074565270467560384*a(n-33) -66023270051350386176*a(n-34) +350852776730555653120*a(n-35) +111115747477690885952*a(n-36) -562968030704836048256*a(n-37) -102780461262027908992*a(n-38) +705293155294335987968*a(n-39) -1905443632362091008*a(n-40) -673839571496082251776*a(n-41) +149968516817181865984*a(n-42) +463807639149162463232*a(n-43) -222954648389494145024*a(n-44) -202119207628642238464*a(n-45) +174410817888004440064*a(n-46) +32943327636122697728*a(n-47) -77835693049096830976*a(n-48) +15691242889927983104*a(n-49) +16793314088391802880*a(n-50) -9742537633650704384*a(n-51) -56226216776040448*a(n-52) +1727131956136640512*a(n-53) -597215426987950080*a(n-54) +331158386638848*a(n-55) +57745072535371776*a(n-56) -19695514744258560*a(n-57) +3305731101032448*a(n-58) -294085000691712*a(n-59) +11132555231232*a(n-60)
%e Some solutions for n=3
%e ..5.-4..1.-4....1.-2..3..0...-6..5.-3..5....3..0.-1.-2...-4..2..0..5
%e .-4..3..0..3...-2..3.-4..1....5.-4..2.-4....0.-3..4.-1....2..0.-2.-3
%e ..1..0.-3..0....3.-4..5.-2...-3..2..0..2...-1..4.-5..2....0.-2..4..1
%e .-4..3..0..3....0..1.-2.-1....5.-4..2.-4...-2.-1..2..1....5.-3..1.-6
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 06 2012
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