A211552 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

180, 504, 1148, 2508, 5202, 10762, 21622, 43984, 87406, 177030, 351096, 711810, 1414930, 2878790, 5747458, 11748876, 23580200, 48449984, 97774376, 201923574, 409657252, 850120676, 1733171824, 3612646782, 7397620764, 15481145862

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) +17*a(n-2) -166*a(n-3) -31*a(n-4) +2043*a(n-5) -1600*a(n-6) -14704*a(n-7) +20269*a(n-8) +68225*a(n-9) -129342*a(n-10) -210658*a(n-11) +529848*a(n-12) +422669*a(n-13) -1504565*a(n-14) -469508*a(n-15) +3056859*a(n-16) -21015*a(n-17) -4491182*a(n-18) +1054426*a(n-19) +4754701*a(n-20) -1955055*a(n-21) -3565976*a(n-22) +2006020*a(n-23) +1829375*a(n-24) -1309433*a(n-25) -598506*a(n-26) +551716*a(n-27) +104454*a(n-28) -144434*a(n-29) -2452*a(n-30) +21200*a(n-31) -2120*a(n-32) -1320*a(n-33) +240*a(n-34)

Example

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

Crossrefs

Sequence in context: A008891 A015233 A307112 * A004532 A143793 A205818

Adjacent sequences: A211549 A211550 A211551 * A211553 A211554 A211555

Keyword

nonn

Author

R. H. Hardin Apr 15 2012

Status

approved