A211816 - OEIS

%I #4 Apr 21 2012 12:15:22

%S 220,602,1368,2942,6088,12442,24924,50194,99390,199570,394162,793028,

%T 1569220,3170790,6300354,12799142,25565534,52235044,104925530,

%U 215604840,435513812,899750556,1827061522,3793414420,7740115362,16142443314

%N Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and 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="/A211816/b211816.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +16*a(n-2) -160*a(n-3) -15*a(n-4) +1883*a(n-5) -1614*a(n-6) -12827*a(n-7) +18643*a(n-8) +55534*a(n-9) -110733*a(n-10) -156457*a(n-11) +420605*a(n-12) +273571*a(n-13) -1096609*a(n-14) -220702*a(n-15) +2018897*a(n-16) -191679*a(n-17) -2645653*a(n-18) +814093*a(n-19) +2453538*a(n-20) -1164914*a(n-21) -1580007*a(n-22) +985631*a(n-23) +680255*a(n-24) -535843*a(n-25) -180672*a(n-26) +188098*a(n-27) +23218*a(n-28) -41026*a(n-29) +676*a(n-30) +5032*a(n-31) -568*a(n-32) -264*a(n-33) +48*a(n-34)

%e Some solutions for n=3

%e .-1..3.-1.-1....6.-2..4.-2...-3.-3.-3..0...-1..2.-1..2....2..1..1..1

%e ..3.-5..3.-1...-2.-2..0.-2...-3..9.-3..6....2.-3..2.-3....1.-4..2.-4

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

%e .-1.-1.-1..3...-2.-2..0.-2....0..6..0..3....2.-3..2.-3....1.-4..2.-4

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 21 2012