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A211330 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values. 1
46, 90, 172, 316, 588, 1070, 1974, 3608, 6670, 12310, 22930, 42818, 80560, 152240, 289462, 553112, 1062084, 2049116, 3968676, 7718410, 15055782, 29469492, 57813502, 113731682, 224119946, 442604110, 875210760, 1733534748, 3436966638 (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) = 5*a(n-1) - a(n-2) - 31*a(n-3) + 39*a(n-4) +  56*a(n-5) - 116*a(n-6) - 14*a(n-7) + 115*a(n-8) - 34*a(n-9) - 30*a(n-10) + 12*a(n-11).

Empirical g.f.: 2*x*(23 - 70*x - 116*x^2 + 486*x^3 + 88*x^4 - 1154*x^5 + 298*x^6 + 1082*x^7 - 466*x^8 - 309*x^9 + 142*x^10) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 17 2018

EXAMPLE

Some solutions for n=3.

.-1..2.-1..0...-5..2.-5..1...-1..2.-1..2....0.-1.-1.-1...-1..2..2..0

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

.-1..2.-1..0...-5..2.-5..1...-1..2.-1..2...-1..0.-2..0....2.-1..5.-3

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

CROSSREFS

Sequence in context: A057454 A260278 A234260 * A121929 A007630 A004923

Adjacent sequences:  A211327 A211328 A211329 * A211331 A211332 A211333

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified August 20 04:46 EDT 2019. Contains 326139 sequences. (Running on oeis4.)