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A224554 Number of (n+2) X 5 0..1 matrices with each 3 X 3 subblock idempotent. 1

%I

%S 113,133,180,230,320,451,620,866,1229,1746,2493,3586,5178,7498,10891,

%T 15855,23117,33749,49321,72130,105545,154505,226246,331373,485430,

%U 711197,1042059,1526945,2237564,3279010,4805306,7042184,10320470,15125013

%N Number of (n+2) X 5 0..1 matrices with each 3 X 3 subblock idempotent.

%C Column 3 of A224559.

%H R. H. Hardin, <a href="/A224554/b224554.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 3*a(n-5) - a(n-6) for n>8.

%F Empirical g.f.: x*(113 - 319*x + 326*x^2 - 257*x^3 + 267*x^4 - 156*x^5 + 20*x^6 + 5*x^7) / ((1 - x)^3*(1 - x - x^3)). - _Colin Barker_, Aug 31 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A224559.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013

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Last modified October 26 21:33 EDT 2021. Contains 348269 sequences. (Running on oeis4.)