A211715 Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two or four distinct values.

34, 58, 106, 202, 394, 778, 1546, 3082, 6154, 12298, 24586, 49162, 98314, 196618, 393226, 786442, 1572874, 3145738, 6291466, 12582922, 25165834, 50331658, 100663306, 201326602, 402653194, 805306378, 1610612746, 3221225482

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) = 3*a(n-1) - 2*a(n-2).

Conjectures from Colin Barker, Jul 19 2018: (Start)

G.f.: 2*x*(17 - 22*x) / ((1 - x)*(1 - 2*x)).

a(n) = 10 + 3*2^(2+n).

(End)

Example

Some solutions for n=3:
..9.-3..3.-9....3..3.-3..3...-6..2.-6..2...-1..1..1.-1...-8..8.-8..8
.-3.-3..3..3....3.-9..9.-9....2..2..2..2....1.-1.-1..1....8.-8..8.-8
..3..3.-3.-3...-3..9.-9..9...-6..2.-6..2....1.-1..3.-3...-8..8.-8..8
.-9..3.-3..9....3.-9..9.-9....2..2..2..2...-1..1.-3..3....8.-8..8.-8

Crossrefs

Sequence in context: A224896 A103558 A103686 * A108610 A261314 A119454

Adjacent sequences: A211712 A211713 A211714 * A211716 A211717 A211718

Keyword

nonn

Author

R. H. Hardin, Apr 20 2012

Status

approved