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A211116 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values. 1
13, 31, 75, 177, 415, 963, 2227, 5137, 11855, 27397, 63483, 147557, 344175, 805635, 1892433, 4460137, 10544415, 24999069, 59419405, 141550383, 337872559, 807871799, 1934541399, 4638401749, 11133523165, 26748531157, 64314484855 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Symmetry and 2 X 2 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) = 7*a(n-1) - 15*a(n-2) + a(n-3) + 33*a(n-4) - 28*a(n-5) - 12*a(n-6) + 16*a(n-7) + a(n-8) - 2*a(n-9).

Empirical g.f.: x*(13 - 60*x + 53*x^2 + 104*x^3 - 159*x^4 - 21*x^5 + 83*x^6 + x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 16 2018

EXAMPLE

Some solutions for n=3:

..2..0..1.-2...-2..0.-2..0....2.-1..2.-1....0.-1.-1..0....2..0..2.-1

..0.-2..1..0....0..2..0..2...-1..0.-1..0...-1..2..0..1....0.-2..0.-1

..1..1..0.-1...-2..0.-2..0....2.-1..2.-1...-1..0.-2..1....2..0..2.-1

.-2..0.-1..2....0..2..0..2...-1..0.-1..0....0..1..1..0...-1.-1.-1..0

CROSSREFS

Sequence in context: A072023 A217614 A158723 * A107288 A335732 A095379

Adjacent sequences:  A211113 A211114 A211115 * A211117 A211118 A211119

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 02 2012

STATUS

approved

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)