cp's OEIS Frontend

A190092 Number of rhombuses on a (n+1) X 4 grid.

%I A190092 #8 May 04 2018 11:51:12
%S A190092 3,10,22,36,50,66,82,100,120,142,164,188,212,238,264,292,320,350,380,
%T A190092 412,444,478,512,548,584,622,660,700,740,782,824,868,912,958,1004,
%U A190092 1052,1100,1150,1200,1252,1304,1358,1412,1468,1524,1582,1640,1700,1760,1822,1884
%N A190092 Number of rhombuses on a (n+1) X 4 grid.
%C A190092 Column 3 of A190098.
%H A190092 R. H. Hardin, <a href="/A190092/b190092.txt">Table of n, a(n) for n = 1..200</a>
%F A190092 Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>11.
%F A190092 Conjectures from _Colin Barker_, May 04 2018: (Start)
%F A190092 G.f.: x*(3 + 4*x + 2*x^2 - 2*x^3 - 5*x^4 + 2*x^8 - 2*x^10) / ((1 - x)^3*(1 + x)).
%F A190092 a(n) = (n^2 + 24*n - 56) / 2 for n>7 and even.
%F A190092 a(n) = (n^2 + 24*n - 57) / 2 for n>7 and odd.
%F A190092 (End)
%e A190092 Some solutions for n=4:
%e A190092 ..0..0....0..2....3..1....1..2....0..0....1..1....3..0....1..0....1..3....0..1
%e A190092 ..1..2....2..1....3..2....2..1....0..1....2..3....3..1....1..2....2..1....1..3
%e A190092 ..3..3....4..2....4..2....3..2....1..1....4..2....4..1....3..2....4..0....3..2
%e A190092 ..2..1....2..3....4..1....2..3....1..0....3..0....4..0....3..0....3..2....2..0
%Y A190092 Cf. A190098.
%K A190092 nonn
%O A190092 1,1
%A A190092 _R. H. Hardin_, May 04 2011