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A211327 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, three or four distinct values. 1
15, 33, 69, 143, 293, 595, 1205, 2427, 4885, 9803, 19669, 39403, 78933, 157995, 316245, 632747, 1266005, 2532523, 5066069, 10133163, 20268373, 40538795, 81081685, 162167467, 324343125, 648694443, 1297405269, 2594826923, 5189686613 (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) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4).

Conjectures from Colin Barker, Jul 17 2018: (Start)

G.f.: x*(15 + 18*x - 24*x^2 - 28*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = (-9*2^(n/2) + 29*2^n + 1)/3 for n even.

a(n) = (-3*2^(n/2+3/2) + 29*2^n - 1)/3 for n odd.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Sequence in context: A228321 A277385 A108517 * A222179 A322493 A190052

Adjacent sequences:  A211324 A211325 A211326 * A211328 A211329 A211330

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)