A211817 Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

221, 623, 1477, 3361, 7389, 16191, 34993, 76417, 165745, 365037, 801507, 1788695, 3988703, 9030407, 20455109, 46942737, 107843925, 250411345, 582132123, 1364670701, 3202526531, 7563851273, 17879861115, 42470025643, 100944212731

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..208

Formula

Empirical: a(n) = 7*a(n-1) +13*a(n-2) -193*a(n-3) +91*a(n-4) +2362*a(n-5) -3292*a(n-6) -16847*a(n-7) +34429*a(n-8) +76986*a(n-9) -209369*a(n-10) -230969*a(n-11) +853727*a(n-12) +433070*a(n-13) -2475538*a(n-14) -365411*a(n-15) +5255855*a(n-16) -451861*a(n-17) -8289963*a(n-18) +2015886*a(n-19) +9768083*a(n-20) -3415078*a(n-21) -8589800*a(n-22) +3606842*a(n-23) +5599559*a(n-24) -2592984*a(n-25) -2671225*a(n-26) +1296044*a(n-27) +912979*a(n-28) -447866*a(n-29) -216050*a(n-30) +104216*a(n-31) +33398*a(n-32) -15468*a(n-33) -3016*a(n-34) +1312*a(n-35) +120*a(n-36) -48*a(n-37)

Example

Some solutions for n=3
.-2.-2.-2.-4..-10..8.-1..3....1..1..1..4....3.-4..3.-2...-5..6.-7..6
.-2..6.-2..8....8.-6.-1.-1....1.-3..1.-6...-4..5.-4..3....6.-7..8.-7
.-2.-2.-2.-4...-1.-1..8.-6....1..1..1..4....3.-4..3.-2...-7..8.-9..8
.-4..8.-4.10....3.-1.-6..4....4.-6..4.-9...-2..3.-2..1....6.-7..8.-7

Crossrefs

Sequence in context: A257752 A147284 A171427 * A157490 A020247 A177422

Adjacent sequences: A211814 A211815 A211816 * A211818 A211819 A211820

Keyword

nonn

Author

R. H. Hardin Apr 21 2012

Status

approved