A194933 - OEIS

%I #9 May 05 2018 20:42:29

%S 1024,5873,12474,19379,26316,33255,40194,47133,54072,61011,67950,

%T 74889,81828,88767,95706,102645,109584,116523,123462,130401,137340,

%U 144279,151218,158157,165096,172035,178974,185913,192852,199791,206730,213669

%N Number of lower triangles of a 4 X 4 0..n array with no element differing from any of its horizontal or vertical neighbors by more than one.

%C Row 4 of A194931.

%H R. H. Hardin, <a href="/A194933/b194933.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6939*n - 8379 for n>4.

%F Empirical g.f.: x*(1024 + 3825*x + 1752*x^2 + 304*x^3 + 32*x^4 + 2*x^5) / (1 - x)^2. - _Colin Barker_, May 05 2018

%e Some solutions for n=4:

%e ..2........0........1........1........2........2........0........2

%e ..1.2......0.1......0.0......2.3......1.2......1.0......0.0......2.1

%e ..2.3.4....0.1.1....1.1.1....3.3.3....1.2.2....0.0.1....1.0.1....2.2.2

%e ..3.3.3.4..0.0.1.1..0.1.1.2..3.2.2.2..0.1.2.1..0.1.2.2..1.0.0.0..2.2.2.3

%Y Cf. A194931.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 05 2011