A211473 Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

144, 1224, 10416, 88776, 757784, 6478064, 55460120, 475479800, 4082006352, 35089391112, 301998774840, 2602109942640, 22443946490552, 193770109394072, 1674359497311056, 14479231995139496, 125296349390355480

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..112

Formula

Empirical: a(n) = 75*a(n-1) -2510*a(n-2) +49200*a(n-3) -622175*a(n-4) +5253075*a(n-5) -29416155*a(n-6) +102987225*a(n-7) -184111448*a(n-8) -476940*a(n-9) +472118829*a(n-10) -56520825*a(n-11) -794496080*a(n-12) -750911850*a(n-13) -339742508*a(n-14) -86830200*a(n-15) -12751696*a(n-16) -999360*a(n-17) -32256*a(n-18)

Example

Some solutions for n=3
.-6..3..1..1....5.-6..3.-2...-8..4.-7..4...-5..3..1..3...-1.-2..1.-3
..3..0.-4..2...-6..7.-4..3....4..0..3..0....3.-1.-3.-1...-2..5.-4..6
..1.-4..8.-6....3.-4..1..0...-7..3.-6..3....1.-3..7.-3....1.-4..3.-5
..1..2.-6..4...-2..3..0.-1....4..0..3..0....3.-1.-3.-1...-3..6.-5..7

Crossrefs

Sequence in context: A235568 A222349 A133062 * A203826 A261655 A203819

Adjacent sequences: A211470 A211471 A211472 * A211474 A211475 A211476

Keyword

nonn

Author

R. H. Hardin Apr 12 2012

Status

approved