A211442 Number of (n+1) X (n+1) -7..7 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.

90, 188, 356, 654, 1190, 2144, 3882, 7028, 12822, 23490, 43364, 80516, 150510, 283054, 535322, 1018120, 1945094, 3734306, 7194586, 13918418, 26998652, 52549144, 102488144, 200438252, 392604464, 770735354, 1514821088, 2982729598

Offset

1,1

Comments

Symmetry and 2 X 2 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) = 4*a(n-1) + 5*a(n-2) - 36*a(n-3) + 6*a(n-4) + 119*a(n-5) - 71*a(n-6) - 180*a(n-7) + 134*a(n-8) + 130*a(n-9) - 90*a(n-10) - 48*a(n-11) + 20*a(n-12) + 8*a(n-13).

Empirical g.f.: 2*x*(45 - 86*x - 423*x^2 + 765*x^3 + 1511*x^4 - 2454*x^5 - 2609*x^6 + 3440*x^7 + 2287*x^8 - 2019*x^9 - 980*x^10 + 412*x^11 + 164*x^12) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2 - x^3)*(1 - 4*x^2 + 2*x^4)). Colin Barker, Jul 17 2018

Example

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

Crossrefs

Sequence in context: A366740 A119896 A179697 * A282473 A044422 A044803

Adjacent sequences: A211439 A211440 A211441 * A211443 A211444 A211445

Keyword

nonn

Author

R. H. Hardin, Apr 11 2012

Status

approved