A211820 Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

220, 2310, 24280, 255510, 2692030, 28396180, 299874470, 3170351150, 33554420380, 355508955450, 3770437474330, 40027054951800, 425319384572170, 4523288178641650, 48144647645503520, 512829600353346710

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..52

Formula

Empirical: a(n) = 114*a(n-1) -5925*a(n-2) +185345*a(n-3) -3877235*a(n-4) +56925919*a(n-5) -597748066*a(n-6) +4472218575*a(n-7) -23123238043*a(n-8) +76099390938*a(n-9) -122330317169*a(n-10) -56591154105*a(n-11) +427598872995*a(n-12) +95124362391*a(n-13) -844404272684*a(n-14) -1140261335975*a(n-15) -728986025396*a(n-16) -278757941362*a(n-17) -67965466156*a(n-18) -10635078240*a(n-19) -1030171920*a(n-20) -55951200*a(n-21) -1296000*a(n-22)

Example

Some solutions for n=3
..7.-7..5..0..-10..1.-7..7....9..0..1.-6....8..0..2.-9....8.-6..2..1
.-7..7.-5..0....1..8.-2..2....0.-9..8.-3....0.-8..6..1...-6..4..0.-3
..5.-5..3..2...-7.-2.-4..4....1..8.-7..2....2..6.-4.-3....2..0.-4..7
..0..0..2.-7....7..2..4.-4...-6.-3..2..3...-9..1.-3.10....1.-3..7-10

Crossrefs

Sequence in context: A233626 A251322 A257353 * A215491 A258537 A027797

Adjacent sequences: A211817 A211818 A211819 * A211821 A211822 A211823

Keyword

nonn

Author

R. H. Hardin Apr 21 2012

Status

approved