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A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

%I A210694 #9 Jul 22 2025 22:31:01
%S A210694 5,13,9,25,35,17,41,91,97,33,61,189,337,275,65,85,341,881,1267,793,
%T A210694 129,113,559,1921,4149,4825,2315,257,145,855,3697,10901,19721,18571,
%U A210694 6817,513,181,1241,6497,24583,62281,94509,72097,20195,1025,221,1729,10657,49575
%N A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.
%C A210694 Table starts
%C A210694 ...5....13.....25......41.......61.......85.......113.......145........181
%C A210694 ...9....35.....91.....189......341......559.......855......1241.......1729
%C A210694 ..17....97....337.....881.....1921.....3697......6497.....10657......16561
%C A210694 ..33...275...1267....4149....10901....24583.....49575.....91817.....159049
%C A210694 ..65...793...4825...19721....62281...164305....379793....793585....1531441
%C A210694 .129..2315..18571...94509...358061..1103479...2920695...6880121...14782969
%C A210694 .257..6817..72097..456161..2070241..7444417..22542017..59823937..143046721
%C A210694 .513.20195.281827.2215269.12030821.50431303.174571335.521638217.1387420489
%C A210694 Solutions are determined by the diagonal, extended with x(i,j) = (x(i,i)+x(j,j))/2 * (-1)^(i-j)
%H A210694 R. H. Hardin, <a href="/A210694/b210694.txt">Table of n, a(n) for n = 1..10000</a>
%F A210694 T(n,k)=k^(n+1)+(k+1)^(n+1)
%e A210694 Some solutions for n=3 k=4
%e A210694 .-2..1.-3..0....0.-1..0..1....4..0..1.-1....2.-1.-1.-2....3.-2..1..0
%e A210694 ..1..0..2..1...-1..2.-1..0....0.-4..3.-3...-1..0..2..1...-2..1..0.-1
%e A210694 .-3..2.-4..1....0.-1..0..1....1..3.-2..2...-1..2.-4..1....1..0.-1..2
%e A210694 ..0..1..1..2....1..0..1.-2...-1.-3..2.-2...-2..1..1..2....0.-1..2.-3
%Y A210694 cf. A179927
%Y A210694 Column 1 is A000051(n+1)
%Y A210694 Column 2 is A007689(n+1)
%Y A210694 Column 3 is A074605(n+1)
%Y A210694 Column 4 is A074611(n+1)
%Y A210694 Column 5 is A074615(n+1)
%Y A210694 Column 6 is A074619(n+1)
%Y A210694 Column 7 is A074622(n+1)
%Y A210694 Column 8 is A074624(n+1)
%Y A210694 Row 1 is A001844
%Y A210694 Row 2 is A005898
%Y A210694 Row 3 is A008514
%Y A210694 Row 4 is A008515
%Y A210694 Row 5 is A008516
%Y A210694 Row 6 is A036085
%Y A210694 Row 7 is A036086
%Y A210694 Row 8 is A036087
%K A210694 nonn,tabl
%O A210694 1,1
%A A210694 _R. H. Hardin_, with R. J. Mathar in the Sequence Fans Mailing List, Mar 30 2012