A211713 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

264, 726, 1670, 3574, 7448, 15136, 30436, 60938, 120832, 241150, 476020, 951586, 1878928, 3771022, 7467440, 15063942, 29958046, 60772582, 121463624, 247803532, 497864910, 1021347926, 2062591634, 4253485786, 8631871242, 17886996814

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..201

Formula

Empirical: a(n) = 5*a(n-1) +23*a(n-2) -149*a(n-3) -196*a(n-4) +2007*a(n-5) +424*a(n-6) -16175*a(n-7) +5683*a(n-8) +87013*a(n-9) -61030*a(n-10) -330011*a(n-11) +313597*a(n-12) +908524*a(n-13) -1043207*a(n-14) -1841180*a(n-15) +2438675*a(n-16) +2754829*a(n-17) -4138459*a(n-18) -3021301*a(n-19) +5162035*a(n-20) +2381895*a(n-21) -4737637*a(n-22) -1297351*a(n-23) +3176171*a(n-24) +447161*a(n-25) -1532186*a(n-26) -72331*a(n-27) +519056*a(n-28) -8146*a(n-29) -118840*a(n-30) +6266*a(n-31) +17252*a(n-32) -1128*a(n-33) -1408*a(n-34) +72*a(n-35) +48*a(n-36)

Example

Some solutions for n=3
.-3..0..0..6...-7..4.-1..4..-11..1.-5..1....6.-8..6.-8....2..2..2.-3
..0..3.-3.-3....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10....2.-6..2.-1
..0.-3..3..3...-1.-2..5.-2...-5.-5..1.-5....6.-8..6.-8....2..2..2.-3
..6.-3..3.-9....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10...-3.-1.-3..4

Crossrefs

Sequence in context: A105683 A160971 A235012 * A185764 A253916 A195672

Adjacent sequences: A211710 A211711 A211712 * A211714 A211715 A211716

Keyword

nonn

Author

R. H. Hardin Apr 20 2012

Status

approved