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A211492 Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. 1
29, 65, 139, 287, 593, 1189, 2397, 4755, 9475, 18743, 37193, 73609, 145989, 289407, 574531, 1141067, 2268401, 4512781, 8983437, 17896131, 35666275, 71126615, 141881945, 283168249, 565251477, 1128785439, 2254414051, 4503880043 (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) = 3*a(n-1) + 5*a(n-2) - 20*a(n-3) - 5*a(n-4) + 45*a(n-5) - 5*a(n-6) - 40*a(n-7) + 6*a(n-8) + 12*a(n-9).

Empirical g.f.: x*(29 - 22*x - 201*x^2 + 125*x^3 + 482*x^4 - 225*x^5 - 480*x^6 + 144*x^7 + 176*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - Colin Barker, Jul 18 2018

EXAMPLE

Some solutions for n=3:

.-1..2.-1..2...-4..2..0..2....2.-1..2.-3....0..2..0..0...-2..3.-2..3

..2.-3..2.-3....2..0.-2..0...-1..0.-1..2....2.-4..2.-2....3.-4..3.-4

.-1..2.-1..2....0.-2..4.-2....2.-1..2.-3....0..2..0..0...-2..3.-2..3

..2.-3..2.-3....2..0.-2..0...-3..2.-3..4....0.-2..0..0....3.-4..3.-4

CROSSREFS

Sequence in context: A240169 A044131 A044512 * A165238 A201022 A118481

Adjacent sequences:  A211489 A211490 A211491 * A211493 A211494 A211495

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 13 2012

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)