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Number of (n+4) X 11 0..2 matrices with each 5 X 5 subblock idempotent.
1

%I #10 Sep 02 2018 17:10:35

%S 54070,31702,36576,39450,41120,42214,50748,64133,80045,97220,115074,

%T 141044,179978,234400,305570,394164,508295,660924,867536,1144876,

%U 1510365,1989537,2620887,3458395,4572786,6052206,8010335,10599348,14025400

%N Number of (n+4) X 11 0..2 matrices with each 5 X 5 subblock idempotent.

%H R. H. Hardin, <a href="/A224624/b224624.txt">Table of n, a(n) for n = 1..51</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) for n>12.

%F Empirical g.f.: x*(54070 - 184578*x + 234188*x^2 - 132922*x^3 + 30038*x^4 - 54238*x^5 + 137896*x^6 - 114285*x^7 + 29507*x^8 + 264*x^9 + 52*x^10 + 5*x^11) / ((1 - x)^3*(1 - x + x^2)*(1 - x^2 - x^3)). - _Colin Barker_, Sep 02 2018

%e Some solutions for n=2:

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

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

%e ..0..0..0..0..0..0..0..0..0..0..0....1..0..0..0..0..1..0..0..0..0..2

%e ..2..0..0..0..0..0..0..0..0..0..0....2..0..0..0..0..1..0..0..0..0..1

%e ..2..0..0..0..0..0..0..0..0..0..1....0..0..0..0..0..1..0..0..0..0..1

%e ..2..0..0..0..0..0..0..0..0..0..1....1..0..0..0..0..1..0..0..0..0..1

%Y Column 7 of A224625.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2013