A211714 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

265, 747, 1781, 4001, 8773, 18947, 40653, 87497, 187925, 408201, 886709, 1954227, 4312823, 9660215, 21682565, 49330249, 112485053, 259451281, 599683373, 1398909233, 3268979199, 7693687203, 18131925659, 42963258607, 101902441855

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) = 8*a(n-1) +6*a(n-2) -206*a(n-3) +285*a(n-4) +2263*a(n-5) -5657*a(n-6) -13373*a(n-7) +50982*a(n-8) +40840*a(n-9) -281579*a(n-10) -13385*a(n-11) +1048034*a(n-12) -436693*a(n-13) -2737159*a(n-14) +2073869*a(n-15) +5090373*a(n-16) -5371714*a(n-17) -6715078*a(n-18) +9215866*a(n-19) +6127230*a(n-20) -11048104*a(n-21) -3615358*a(n-22) +9411386*a(n-23) +1097124*a(n-24) -5704954*a(n-25) +102275*a(n-26) +2442605*a(n-27) -246701*a(n-28) -727226*a(n-29) +105622*a(n-30) +146470*a(n-31) -22910*a(n-32) -18988*a(n-33) +2584*a(n-34) +1432*a(n-35) -120*a(n-36) -48*a(n-37)

Example

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

Crossrefs

Sequence in context: A051976 A255085 A146335 * A259741 A202416 A202471

Adjacent sequences: A211711 A211712 A211713 * A211715 A211716 A211717

Keyword

nonn

Author

R. H. Hardin Apr 20 2012

Status

approved