A213698 Half the number of 3 X 3 0..n symmetric arrays with no 2 X 2 subblock summing to 2n.

13, 192, 1320, 5470, 17499, 45892, 105856, 219564, 421825, 758560, 1296408, 2117882, 3336655, 5087460, 7549184, 10927192, 15486741, 21525024, 29417800, 39578070, 52519203, 68796772, 89091840, 114132100, 144799369, 182025792

Offset: 1

Author

R. H. Hardin, Jun 18 2012

Keywords

• nonn

Comments

Row 2 of A213697.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A213697.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).

Empirical g.f.: x*(13 + 153*x + 731*x^2 + 1461*x^3 + 1803*x^4 + 1111*x^5 + 425*x^6 + 59*x^7 + 4*x^8) / ((1 - x)^7*(1 + x)^4). - Colin Barker, Jul 22 2018