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A211556 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values 1
180, 1712, 16318, 155904, 1492928, 14327826, 137797604, 1327935624, 12821402190, 124011705656, 1201438512040, 11657189258802, 113261149760588, 1101805278189552, 10730222804297534, 104601472189182192 (list; graph; refs; listen; history; text; internal format)
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..54

FORMULA

Empirical: a(n) = 94*a(n-1) -3990*a(n-2) +100725*a(n-3) -1674425*a(n-4) +19135732*a(n-5) -151829733*a(n-6) +819081545*a(n-7) -2798053008*a(n-8) +4813088305*a(n-9) +909604521*a(n-10) -14434966072*a(n-11) -404287970*a(n-12) +26746796493*a(n-13) +30215600922*a(n-14) +16403931314*a(n-15) +5216836244*a(n-16) +1016849976*a(n-17) +119142480*a(n-18) +7668288*a(n-19) +207360*a(n-20)

EXAMPLE

Some solutions for n=3

..8..0..6.-2...-8..5.-7..2....1.-1..0..3....5.-3..6..2....1.-1..4..2

..0.-8..2.-6....5.-2..4..1...-1..1..0.-3...-3..1.-4.-4...-1..1.-4.-2

..6..2..4..0...-7..4.-6..1....0..0.-1..4....6.-4..7..1....4.-4..7.-1

.-2.-6..0.-4....2..1..1..4....3.-3..4.-7....2.-4..1.-9....2.-2.-1.-5

CROSSREFS

Sequence in context: A081380 A115184 A154672 * A184225 A099106 A179721

Adjacent sequences:  A211553 A211554 A211555 * A211557 A211558 A211559

KEYWORD

nonn

AUTHOR

R. H. Hardin Apr 15 2012

STATUS

approved

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Last modified September 20 23:04 EDT 2021. Contains 347596 sequences. (Running on oeis4.)