cp's OEIS Frontend

A190091 Number of rhombuses on a (n+1) X 3 grid.

%I A190091 #9 May 04 2018 11:43:19
%S A190091 2,6,10,15,20,26,32,39,46,54,62,71,80,90,100,111,122,134,146,159,172,
%T A190091 186,200,215,230,246,262,279,296,314,332,351,370,390,410,431,452,474,
%U A190091 496,519,542,566,590,615,640,666,692,719,746,774,802,831,860,890,920,951,982
%N A190091 Number of rhombuses on a (n+1) X 3 grid.
%C A190091 Column 2 of A190098.
%H A190091 R. H. Hardin, <a href="/A190091/b190091.txt">Table of n, a(n) for n = 1..200</a>
%F A190091 Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
%F A190091 Conjectures from _Colin Barker_, May 04 2018: (Start)
%F A190091 G.f.: x*(2 + 2*x - 2*x^2 - x^3) / ((1 - x)^3*(1 + x)).
%F A190091 a(n) = (n^2 + 12*n - 4) / 4 for n even.
%F A190091 a(n) = (n^2 + 12*n - 5) / 4 for n odd.
%F A190091 (End)
%e A190091 All solutions for n=3:
%e A190091 ..0..1....2..0....0..1....1..1....1..1....1..0....0..0....0..0....2..1....1..0
%e A190091 ..1..0....2..1....0..2....2..0....1..2....1..2....0..1....0..2....2..2....1..1
%e A190091 ..2..1....3..1....1..2....3..1....2..2....3..2....1..1....2..2....3..2....2..1
%e A190091 ..1..2....3..0....1..1....2..2....2..1....3..0....1..0....2..0....3..1....2..0
%Y A190091 Cf. A190098.
%K A190091 nonn
%O A190091 1,1
%A A190091 _R. H. Hardin_, May 04 2011