A211467 Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and three distinct values

120, 260, 508, 940, 1734, 3126, 5690, 10276, 18758, 34230, 63068, 116594, 217310, 407026, 767450, 1454628, 2771646, 5306940, 10202586, 19697838, 38146332, 74135060, 144403432, 282088738, 551970304, 1082582606, 2125859552, 4182450010

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) = 4*a(n-1) +9*a(n-2) -52*a(n-3) -16*a(n-4) +271*a(n-5) -86*a(n-6) -724*a(n-7) +435*a(n-8) +1052*a(n-9) -760*a(n-10) -817*a(n-11) +575*a(n-12) +320*a(n-13) -150*a(n-14) -60*a(n-15)

Example

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

Crossrefs

Sequence in context: A028976 A158130 A070856 * A257712 A250607 A076579

Adjacent sequences: A211464 A211465 A211466 * A211468 A211469 A211470

Keyword

nonn

Author

R. H. Hardin Apr 12 2012

Status

approved