A211556 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

180, 1712, 16318, 155904, 1492928, 14327826, 137797604, 1327935624, 12821402190, 124011705656, 1201438512040, 11657189258802, 113261149760588, 1101805278189552, 10730222804297534, 104601472189182192

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..54

Formula

Empirical: a(n) = 94*a(n-1) -3990*a(n-2) +100725*a(n-3) -1674425*a(n-4) +19135732*a(n-5) -151829733*a(n-6) +819081545*a(n-7) -2798053008*a(n-8) +4813088305*a(n-9) +909604521*a(n-10) -14434966072*a(n-11) -404287970*a(n-12) +26746796493*a(n-13) +30215600922*a(n-14) +16403931314*a(n-15) +5216836244*a(n-16) +1016849976*a(n-17) +119142480*a(n-18) +7668288*a(n-19) +207360*a(n-20)

Example

Some solutions for n=3
..8..0..6.-2...-8..5.-7..2....1.-1..0..3....5.-3..6..2....1.-1..4..2
..0.-8..2.-6....5.-2..4..1...-1..1..0.-3...-3..1.-4.-4...-1..1.-4.-2
..6..2..4..0...-7..4.-6..1....0..0.-1..4....6.-4..7..1....4.-4..7.-1
.-2.-6..0.-4....2..1..1..4....3.-3..4.-7....2.-4..1.-9....2.-2.-1.-5

Crossrefs

Sequence in context: A081380 A115184 A154672 * A364162 A184225 A099106

Adjacent sequences: A211553 A211554 A211555 * A211557 A211558 A211559

Keyword

nonn

Author

R. H. Hardin Apr 15 2012

Status

approved