cp's OEIS Frontend

A194999 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

%I A194999 #9 May 06 2018 11:54:44
%S A194999 2,20,42,66,90,114,138,162,186,210,234,258,282,306,330,354,378,402,
%T A194999 426,450,474,498,522,546,570,594,618,642,666,690,714,738,762,786,810,
%U A194999 834,858,882,906,930,954,978,1002,1026,1050,1074,1098,1122,1146,1170,1194,1218
%N A194999 Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its horizontal and vertical neighbors by one.
%C A194999 Row 3 of A194998.
%H A194999 R. H. Hardin, <a href="/A194999/b194999.txt">Table of n, a(n) for n = 1..200</a>
%F A194999 Empirical: a(n) = 24*n - 30 for n>2.
%F A194999 Empirical g.f.: 2*x*(1 + 8*x + 2*x^2 + x^3) / (1 - x)^2. - _Colin Barker_, May 06 2018
%e A194999 Some solutions for n=4:
%e A194999 ..2......0......4......1......2......1......4......2......3......1......4
%e A194999 ..3.2....1.2....3.2....2.1....1.2....2.3....3.4....1.2....4.3....2.3....3.2
%e A194999 ..4.3.4..2.1.0..4.3.4..3.2.3..0.1.2..3.2.3..2.3.4..0.1.0..3.2.1..3.2.1..2.1.0
%Y A194999 Cf. A194998.
%K A194999 nonn
%O A194999 1,1
%A A194999 _R. H. Hardin_, Sep 07 2011