A213698 - OEIS

%I #8 Jul 22 2018 06:42:10

%S 13,192,1320,5470,17499,45892,105856,219564,421825,758560,1296408,

%T 2117882,3336655,5087460,7549184,10927192,15486741,21525024,29417800,

%U 39578070,52519203,68796772,89091840,114132100,144799369,182025792

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

%C Row 2 of A213697.

%H R. H. Hardin, <a href="/A213698/b213698.txt">Table of n, a(n) for n = 1..210</a>

%F 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).

%F 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

%e Some solutions for n=4:

%e ..0..3..4....2..0..1....0..1..1....4..4..4....3..0..0....2..4..3....3..1..1

%e ..3..0..3....0..2..0....1..3..2....4..1..2....0..1..4....4..3..2....1..2..0

%e ..4..3..3....1..0..0....1..2..4....4..2..4....0..4..2....3..2..2....1..0..2

%Y Cf. A213697.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 18 2012