A211490 Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.

13, 17, 23, 33, 49, 75, 117, 185, 295, 473, 761, 1227, 1981, 3201, 5175, 8369, 13537, 21899, 35429, 57321, 92743, 150057, 242793, 392843, 635629, 1028465, 1664087, 2692545, 4356625, 7049163, 11405781, 18454937, 29860711, 48315641, 78176345

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) = 2*a(n-1) - a(n-3).

Conjectures from Colin Barker, Jul 18 2018: (Start)

G.f.: x*(13 - 9*x - 11*x^2) / ((1 - x)*(1 - x - x^2)).

a(n) = 7 + (2^(1-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).

(End)

Example

Some solutions for n=3:
.-2..2.-2..2....0..0..0..0....1.-1.-1.-1....4.-4..4.-4...-3..1.-1..3
..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....1..1.-1.-1
.-2..2.-2..2....0..0..0..0...-1..1.-3..1....4.-4..4.-4...-1.-1..1..1
..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....3.-1..1.-3

Crossrefs

Sequence in context: A143822 A172096 A022893 * A038680 A227916 A158072

Adjacent sequences: A211487 A211488 A211489 * A211491 A211492 A211493

Keyword

nonn

Author

R. H. Hardin, Apr 13 2012

Status

approved