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 A211714 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values 1

%I #4 Apr 20 2012 06:20:55

%S 265,747,1781,4001,8773,18947,40653,87497,187925,408201,886709,

%T 1954227,4312823,9660215,21682565,49330249,112485053,259451281,

%U 599683373,1398909233,3268979199,7693687203,18131925659,42963258607,101902441855

%N Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one, two 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="/A211714/b211714.txt">Table of n, a(n) for n = 1..201</a>

%F Empirical: a(n) = 8*a(n-1) +6*a(n-2) -206*a(n-3) +285*a(n-4) +2263*a(n-5) -5657*a(n-6) -13373*a(n-7) +50982*a(n-8) +40840*a(n-9) -281579*a(n-10) -13385*a(n-11) +1048034*a(n-12) -436693*a(n-13) -2737159*a(n-14) +2073869*a(n-15) +5090373*a(n-16) -5371714*a(n-17) -6715078*a(n-18) +9215866*a(n-19) +6127230*a(n-20) -11048104*a(n-21) -3615358*a(n-22) +9411386*a(n-23) +1097124*a(n-24) -5704954*a(n-25) +102275*a(n-26) +2442605*a(n-27) -246701*a(n-28) -727226*a(n-29) +105622*a(n-30) +146470*a(n-31) -22910*a(n-32) -18988*a(n-33) +2584*a(n-34) +1432*a(n-35) -120*a(n-36) -48*a(n-37)

%e Some solutions for n=3

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

%e ..4.-6..4.-1....5-11..5.-7....2.-4..2.-2...-3..5.-1.-3...-4..5.-4..5

%e .-2..4.-2.-1....1..5..1..1....0..2..0..0...-1.-1.-3..7....3.-4..3.-4

%e .-1.-1.-1..4....1.-7..1.-3....0.-2..0..0....5.-3..7-11...-4..5.-4..5

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 20 2012

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Last modified September 29 16:44 EDT 2023. Contains 365773 sequences. (Running on oeis4.)