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A224553 Number of (n+2) X 4 0..1 matrices with each 3 X 3 subblock idempotent. 1

%I #9 Apr 20 2020 21:15:01

%S 70,94,133,174,246,351,492,693,992,1418,2036,2937,4253,6169,8973,

%T 13073,19074,27857,40723,59566,87173,127620,186889,273737,401009,

%U 587520,860854,1261428,1848486,2708844,3969747,5817672,8525924,12495041,18312050

%N Number of (n+2) X 4 0..1 matrices with each 3 X 3 subblock idempotent.

%C Column 2 of A224559.

%H R. H. Hardin, <a href="/A224553/b224553.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - a(n-5) + 2*a(n-6) - a(n-7) for n>9.

%F Empirical g.f.: x*(70 - 116*x - 9*x^2 + 33*x^3 + 14*x^4 + 70*x^5 - 74*x^6 + 6*x^7 + 4*x^8) / ((1 - x)^3*(1 + x)*(1 - x - x^3)). - _Colin Barker_, Aug 31 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A224559.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)