A211551 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

151, 347, 697, 1351, 2573, 4843, 9101, 17119, 32217, 61049, 115711, 221303, 423135, 816445, 1574315, 3060679, 5945293, 11628771, 22724533, 44657457, 87680827, 172920419, 340748827, 673800359, 1331438461, 2638045435, 5223798103

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) = 4*a(n-1) +11*a(n-2) -60*a(n-3) -34*a(n-4) +375*a(n-5) -53*a(n-6) -1270*a(n-7) +601*a(n-8) +2541*a(n-9) -1636*a(n-10) -3075*a(n-11) +2204*a(n-12) +2210*a(n-13) -1562*a(n-14) -875*a(n-15) +530*a(n-16) +150*a(n-17) -60*a(n-18)

Example

Some solutions for n=3
..8.-2..8.-3....5.-7.-1.-7....5.-1..5.-2...-1..4..4..4....3.-5..3.-5
.-2.-4.-2.-3...-7..9.-1..9...-1.-3.-1.-2....4.-7.-1.-7...-5..7.-5..7
..8.-2..8.-3...-1.-1.-7.-1....5.-1..5.-2....4.-1..9.-1....3.-5..3.-5
.-3.-3.-3.-2...-7..9.-1..9...-2.-2.-2.-1....4.-7.-1.-7...-5..7.-5..7

Crossrefs

Sequence in context: A031893 A118494 A140022 * A108842 A078858 A217498

Adjacent sequences: A211548 A211549 A211550 * A211552 A211553 A211554

Keyword

nonn

Author

R. H. Hardin Apr 15 2012

Status

approved