cp's OEIS Frontend

A224671 Number of (n+1) X 4 0..2 matrices with each 2 X 2 subblock idempotent.

%I A224671 #7 Feb 17 2018 05:32:30
%S A224671 41,76,108,170,257,398,617,967,1525,2421,3862,6185,9934,15990,25778,
%T A224671 41604,67199,108600,175575,283929,459235,742871,1201788,1944315,
%U A224671 3145732,5089648,8234952,13324142,21558605,34882226,56440277,91321915,147761569
%N A224671 Number of (n+1) X 4 0..2 matrices with each 2 X 2 subblock idempotent.
%C A224671 Column 3 of A224676.
%H A224671 R. H. Hardin, <a href="/A224671/b224671.txt">Table of n, a(n) for n = 1..210</a>
%F A224671 Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6.
%F A224671 Conjectures from _Colin Barker_, Feb 17 2018: (Start)
%F A224671 G.f.: x*(41 - 88*x + 9*x^2 + 77*x^3 - 41*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)).
%F A224671 a(n) = 5 + (2^(-1-n)*((1-sqrt(5))^n*(-19+29*sqrt(5)) + (1+sqrt(5))^n*(19+29*sqrt(5)))) / sqrt(5) + 4*(1+n) + (1+n)*(2+n)/2 for n>1.
%F A224671 (End)
%e A224671 Some solutions for n=3:
%e A224671 ..1..1..1..0....1..0..1..0....1..1..1..2....0..0..0..0....1..1..0..0
%e A224671 ..0..0..0..0....1..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A224671 ..1..1..1..1....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..0
%e A224671 ..0..0..0..0....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..1
%K A224671 nonn
%O A224671 1,1
%A A224671 _R. H. Hardin_, Apr 14 2013