A211327 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, three or four distinct values.

15, 33, 69, 143, 293, 595, 1205, 2427, 4885, 9803, 19669, 39403, 78933, 157995, 316245, 632747, 1266005, 2532523, 5066069, 10133163, 20268373, 40538795, 81081685, 162167467, 324343125, 648694443, 1297405269, 2594826923, 5189686613

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) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4).

Conjectures from Colin Barker, Jul 17 2018: (Start)

G.f.: x*(15 + 18*x - 24*x^2 - 28*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = (-9*2^(n/2) + 29*2^n + 1)/3 for n even.

a(n) = (-3*2^(n/2+3/2) + 29*2^n - 1)/3 for n odd.

(End)

Example

Some solutions for n=3:
.-1..2..1..0....0.-1..0.-1...-2..1..0..1....1.-2..1.-2....0..0..0..0
..2.-3..0.-1...-1..2.-1..2....1..0.-1..0...-2..3.-2..3....0..0..0..0
..1..0..3.-2....0.-1..0.-1....0.-1..2.-1....1.-2..1.-2....0..0..0..0
..0.-1.-2..1...-1..2.-1..2....1..0.-1..0...-2..3.-2..3....0..0..0..0

Crossrefs

Sequence in context: A228321 A277385 A108517 * A222179 A322493 A190052

Adjacent sequences: A211324 A211325 A211326 * A211328 A211329 A211330

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved