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One-third of the number of n X n nonnegative integer arrays with every 3 X 3 subblock summing to 1.
0

%I #15 Apr 23 2015 13:42:56

%S 3,7,11,15,27,39,51,87,123,159,267,375,483,807,1131,1455,2427,3399,

%T 4371,7287,10203,13119,21867,30615

%N One-third of the number of n X n nonnegative integer arrays with every 3 X 3 subblock summing to 1.

%C First differences of (a(3k), a(3k + 1)), (a(3k + 1), a(3k + 2)), (a(3k + 2), a(3k + 3)) seem to be 4 * 3^(k - 1). - _David A. Corneth_, Apr 15 2015

%F Conjectured g.f.: x^3*(3 + 4*x+ 4*x^2 - 5*x^3)/(1 - x - 3*x^3 + 3*x^4). - _Alexander R. Povolotsky_, Apr 15 2015

%F Conjectured formula: a(n) = 6*(3^(floor(n / 3))/3 - 1) + 3 + 4 * (n mod 3) * 3^(floor(n / 3))/3. - _David A. Corneth_, Apr 15 2015

%K nonn

%O 3,1

%A _R. H. Hardin_, Sep 30 2008