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%I #9 Jan 05 2025 19:51:40
%S 122,272,482,666,1202,2092,3308,5398,8876,14232,22734,36346,57712,
%T 91204,143828,226126,354436,554296,865004,1347042,2093774,3248860,
%U 5032926,7784734,12023856,18546144
%N Number of (n+2)X(n+2) 0..2 matrices with each 3X3 subblock idempotent
%C Diagonal of A224606
%H Christian Ballot, Clark Kimberling, and Peter J. C. Moses, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/55-5/BallotKimberlingMoses.pdf">Linear Recurrences Originating From Polynomial Trees</a>, Fibonacci Quart. 55 (2017), no. 5, 15-27. Mentions this sequence.
%F Empirical: a(n) = 6*a(n-1) -15*a(n-2) +23*a(n-3) -30*a(n-4) +36*a(n-5) -34*a(n-6) +27*a(n-7) -21*a(n-8) +13*a(n-9) -6*a(n-10) +3*a(n-11) -a(n-12) for n>14
%e Some solutions for n=3
%e ..1..0..0..0..0....0..1..0..0..2....1..1..1..0..2....1..1..1..0..1
%e ..1..0..0..0..0....0..1..0..0..1....0..0..0..0..0....0..0..0..0..0
%e ..1..0..0..0..0....0..1..0..0..1....0..0..0..0..0....0..0..0..0..0
%e ..2..0..0..0..0....0..1..0..0..1....0..0..0..0..0....2..1..1..1..1
%e ..1..0..0..0..0....0..2..0..0..1....0..2..1..1..1....0..0..0..0..0
%K nonn,changed
%O 1,1
%A _R. H. Hardin_, Apr 11 2013