cp's OEIS Frontend

A194616 Half the number of lower triangles of a 3X3 0..n array with no element equal to the average of its horizontal and vertical neighbors.

%I A194616 #8 Jun 03 2025 15:34:04
%S A194616 5,96,775,3638,12438,34247,82057,175111,344173,630849,1094898,1812250,
%T A194616 2887675,4445870,6653357,9703428,13843860,19356297,26596343,35955433,
%U A194616 47921851,63027619,81920692,105300352,134012453,168951880,211194991
%N A194616 Half the number of lower triangles of a 3X3 0..n array with no element equal to the average of its horizontal and vertical neighbors.
%C A194616 Row 2 of A194615
%H A194616 R. H. Hardin, <a href="/A194616/b194616.txt">Table of n, a(n) for n = 1..200</a>
%F A194616 Empirical: a(n) = -a(n-1) +a(n-3) +2*a(n-4) +3*a(n-5) +3*a(n-6) +a(n-7) -2*a(n-8) -5*a(n-9) -6*a(n-10) -6*a(n-11) -2*a(n-12) +2*a(n-13) +5*a(n-14) +7*a(n-15) +6*a(n-16) +2*a(n-17) -2*a(n-18) -4*a(n-19) -4*a(n-20) -a(n-21) +a(n-22) +4*a(n-23) +4*a(n-24) +2*a(n-25) -2*a(n-26) -6*a(n-27) -7*a(n-28) -5*a(n-29) -2*a(n-30) +2*a(n-31) +6*a(n-32) +6*a(n-33) +5*a(n-34) +2*a(n-35) -a(n-36) -3*a(n-37) -3*a(n-38) -2*a(n-39) -a(n-40) +a(n-42) +a(n-43)
%e A194616 Some solutions for n=2
%e A194616 ..2......2......1......1......1......2......0......1......2......0......2
%e A194616 ..0.2....1.0....0.2....0.2....2.2....0.2....2.0....0.2....0.2....1.0....1.1
%e A194616 ..1.0.1..0.1.2..2.1.0..1.0.1..0.1.0..2.0.2..0.2.0..1.1.2..1.1.2..2.1.2..1.0.1
%K A194616 nonn
%O A194616 1,1
%A A194616 _R. H. Hardin_ Aug 30 2011