A211494 Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

41, 105, 259, 619, 1455, 3389, 7821, 18047, 41509, 95753, 220953, 511805, 1187991, 2768195, 6468085, 15166639, 35663339, 84116703, 198906647, 471540601, 1120285205, 2667019663, 6360447181, 15193138613, 36342090585, 87038546365

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..210

Formula

Empirical: a(n) = 6*a(n-1) +2*a(n-2) -73*a(n-3) +72*a(n-4) +364*a(n-5) -568*a(n-6) -954*a(n-7) +1943*a(n-8) +1391*a(n-9) -3685*a(n-10) -1073*a(n-11) +4101*a(n-12) +326*a(n-13) -2657*a(n-14) +54*a(n-15) +953*a(n-16) -47*a(n-17) -172*a(n-18) +6*a(n-19) +12*a(n-20)

Example

Some solutions for n=3
.-1..0.-1..2....1..1..1..0...-2..0.-2..1....4.-2..2..0....2.-1..0.-1
..0..1..0.-1....1.-3..1.-2....0..2..0..1...-2..0..0.-2...-1..0..1..0
.-1..0.-1..2....1..1..1..0...-2..0.-2..1....2..0..0..2....0..1.-2..1
..2.-1..2.-3....0.-2..0.-1....1..1..1..0....0.-2..2.-4...-1..0..1..0

Crossrefs

Sequence in context: A115163 A044228 A044609 * A142054 A279213 A070270

Adjacent sequences: A211491 A211492 A211493 * A211495 A211496 A211497

Keyword

nonn

Author

R. H. Hardin Apr 13 2012

Status

approved