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A211712 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values 1
231, 537, 1099, 2099, 3997, 7379, 13747, 25335, 47093, 87513, 163699, 307721, 581223, 1105495, 2109715, 4055319, 7812709, 15150193, 29420803, 57448799, 112272663, 220389539, 432816337, 852950837, 1681246791, 3322791067 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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)

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 5*a(n-1) +9*a(n-2) -80*a(n-3) +9*a(n-4) +535*a(n-5) -425*a(n-6) -1941*a(n-7) +2321*a(n-8) +4142*a(n-9) -6337*a(n-10) -5243*a(n-11) +10073*a(n-12) +3703*a(n-13) -9603*a(n-14) -1139*a(n-15) +5360*a(n-16) -87*a(n-17) -1632*a(n-18) +123*a(n-19) +238*a(n-20) -18*a(n-21) -12*a(n-22)

EXAMPLE

Some solutions for n=3

..3..0..3..0....5.-1.-3.-1...-1..3..1..0....1..3..2..3...10.-6.10.-2

..0.-3..0.-3...-1.-3..7.-3....3.-5..1.-2....3.-7..2.-7...-6..2.-6.-2

..3..0..3..0...-3..7-11..7....1..1..3.-2....2..2..3..2...10.-6.10.-2

..0.-3..0.-3...-1.-3..7.-3....0.-2.-2..1....3.-7..2.-7...-2.-2.-2.-6

CROSSREFS

Sequence in context: A046009 A117223 A160355 * A324315 A276832 A324319

Adjacent sequences:  A211709 A211710 A211711 * A211713 A211714 A211715

KEYWORD

nonn

AUTHOR

R. H. Hardin Apr 20 2012

STATUS

approved

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Last modified June 5 16:30 EDT 2020. Contains 334852 sequences. (Running on oeis4.)