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A190093 Number of rhombuses on an (n+1) X 5 grid.

%I A190093 #8 May 04 2018 12:04:35
%S A190093 4,15,36,66,96,130,164,204,248,296,344,396,448,504,560,620,680,744,
%T A190093 808,876,944,1016,1088,1164,1240,1320,1400,1484,1568,1656,1744,1836,
%U A190093 1928,2024,2120,2220,2320,2424,2528,2636,2744,2856,2968,3084,3200,3320,3440
%N A190093 Number of rhombuses on an (n+1) X 5 grid.
%C A190093 Column 4 of A190098.
%H A190093 R. H. Hardin, <a href="/A190093/b190093.txt">Table of n, a(n) for n = 1..200</a>
%F A190093 Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>11.
%F A190093 Conjectures from _Colin Barker_, May 04 2018: (Start)
%F A190093 G.f.: x*(4 + 7*x + 6*x^2 + 2*x^3 - 10*x^4 - 5*x^5 + 2*x^7 + 4*x^8 - 2*x^9 - 4*x^10) / ((1 - x)^3*(1 + x)).
%F A190093 a(n) = n^2 + 28*n - 84 for n>7 and even.
%F A190093 a(n) = n^2 + 28*n - 85 for n>7 and odd.
%F A190093 (End)
%e A190093 Some solutions for n=3:
%e A190093 ..1..2....2..3....0..3....0..0....0..1....0..0....2..0....1..2....0..1....1..2
%e A190093 ..1..4....2..4....1..2....0..3....1..3....1..2....2..1....2..0....0..4....2..1
%e A190093 ..3..4....3..4....2..3....3..3....3..2....3..3....3..1....3..2....3..4....3..2
%e A190093 ..3..2....3..3....1..4....3..0....2..0....2..1....3..0....2..4....3..1....2..3
%Y A190093 Cf. A190098.
%K A190093 nonn
%O A190093 1,1
%A A190093 _R. H. Hardin_, May 04 2011