cp's OEIS Frontend

A259215 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259215 #10 Dec 24 2018 08:46:52
%S A259215 7,13,24,45,85,162,311,601,1168,2281,4473,8802,17371,34365,68120,
%T A259215 135253,268909,535234,1066287,2125809,4240672,8463633,16898609,
%U A259215 33750850,67426675,134731957,269267496,538217181,1075920133,2151008226,4300670183
%N A259215 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259215 R. H. Hardin, <a href="/A259215/b259215.txt">Table of n, a(n) for n = 1..210</a>
%F A259215 Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).
%F A259215 Conjectures from _Colin Barker_, Dec 24 2018: (Start)
%F A259215 G.f.: x*(7 - 8*x - 8*x^2) / ((1 - 2*x)*(1 - x - x^2)).
%F A259215 a(n) = 2^(1+n) + (2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
%F A259215 (End)
%e A259215 Some solutions for n=4:
%e A259215 ..1..0....0..1....1..1....0..1....1..0....0..1....0..0....1..0....1..0....0..0
%e A259215 ..0..1....1..0....0..0....0..1....0..1....1..0....0..0....0..1....1..0....0..0
%e A259215 ..0..1....0..1....1..1....1..0....0..1....0..1....1..1....0..1....0..1....0..0
%e A259215 ..1..0....1..0....0..0....1..0....0..1....1..0....0..0....1..0....1..0....1..1
%e A259215 ..0..1....0..1....1..1....0..1....1..0....1..0....1..1....1..0....1..0....0..0
%Y A259215 Column 1 of A259222.
%K A259215 nonn
%O A259215 1,1
%A A259215 _R. H. Hardin_, Jun 21 2015