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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 1
144, 1224, 10416, 88776, 757784, 6478064, 55460120, 475479800, 4082006352, 35089391112, 301998774840, 2602109942640, 22443946490552, 193770109394072, 1674359497311056, 14479231995139496, 125296349390355480 (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..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

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Last modified August 4 18:51 EDT 2020. Contains 336202 sequences. (Running on oeis4.)