A211258 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and three or four distinct values

64, 322, 1602, 7994, 39770, 197618, 980042, 4851354, 23971042, 118229026, 582129930, 2861563514, 14044992402, 68835873986, 336921033210, 1647038902058, 8042362627394, 39229027769714, 191167187783274, 930758796100442

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) = 13*a(n-1) +13*a(n-2) -721*a(n-3) +779*a(n-4) +18689*a(n-5) -25301*a(n-6) -297919*a(n-7) +287578*a(n-8) +3113878*a(n-9) -880464*a(n-10) -20368976*a(n-11) -8788232*a(n-12) +71301440*a(n-13) +72542540*a(n-14) -93705748*a(n-15) -122099536*a(n-16) +82149632*a(n-17) +97618464*a(n-18) -62699504*a(n-19) -36898656*a(n-20) +34352128*a(n-21) +226560*a(n-22) -8062208*a(n-23) +3326976*a(n-24) -568320*a(n-25) +36864*a(n-26)

Example

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

Crossrefs

Sequence in context: A221486 A231942 A221686 * A252080 A017366 A186441

Adjacent sequences: A211255 A211256 A211257 * A211259 A211260 A211261

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved