login
Number of (n+1) X 6 0..1 matrices with each 2 X 2 subblock idempotent.
1

%I #7 Aug 30 2018 15:03:16

%S 80,137,193,294,428,635,943,1420,2162,3333,5193,8166,12936,20611,

%T 32983,52952,85210,137349,221653,357998,578544,935327,1512543,2446424,

%U 3957398,6402125,10357693,16757850,27113432,43869023,70980043,114846496

%N Number of (n+1) X 6 0..1 matrices with each 2 X 2 subblock idempotent.

%C Column 5 of A224550.

%H R. H. Hardin, <a href="/A224547/b224547.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Empirical g.f.: x*(80 - 183*x + 45*x^2 + 127*x^3 - 80*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Aug 30 2018

%e Some solutions for n=3:

%e ..1..1..1..1..0..1....1..0..0..1..0..1....1..0..0..0..0..0....1..1..0..0..0..1

%e ..0..0..0..0..0..1....1..0..0..1..0..1....0..0..0..0..0..0....0..0..0..0..0..1

%e ..0..0..0..0..0..1....0..0..0..1..0..1....0..0..0..0..0..0....0..0..0..0..0..1

%e ..0..0..0..0..0..1....0..0..0..1..0..1....0..0..0..0..1..1....0..0..0..0..0..1

%Y Cf. A224550.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013