cp's OEIS Frontend

A221121 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

%I A221121 #8 Aug 03 2018 16:33:57
%S A221121 8,200,4872,118472,2880520,70036168,1702839048,41402332360,
%T A221121 1006644240392,24475254623432,595084206353160,14468703925621448,
%U A221121 351787849605678088,8553267228797150920,207961646114893122312,5056318842606537992392
%N A221121 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.
%C A221121 Column 3 of A221125.
%H A221121 R. H. Hardin, <a href="/A221121/b221121.txt">Table of n, a(n) for n = 1..124</a>
%F A221121 Empirical: a(n) = 26*a(n-1) - 41*a(n-2).
%F A221121 Conjectures from _Colin Barker_, Aug 03 2018: (Start)
%F A221121 G.f.: 8*x*(1 - x) / (1 - 26*x + 41*x^2).
%F A221121 a(n) = ((13-8*sqrt(2))^n*(4-7*sqrt(2)) + (4+7*sqrt(2))*(13+8*sqrt(2))^n) / 41.
%F A221121 (End)
%e A221121 Some solutions for n=3.
%e A221121 ..2..1..0....2..1..0....1..1..1....1..1..0....1..0..1....0..1..1....1..2..0
%e A221121 ..0..4..0....2..1..0....0..2..0....2..1..0....1..2..0....1..2..0....1..1..0
%e A221121 ..1..0..1....2..0..1....3..0..1....3..1..0....2..1..1....1..1..2....1..3..0
%Y A221121 Cf. A221125.
%K A221121 nonn
%O A221121 1,1
%A A221121 _R. H. Hardin_, Jan 02 2013