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 A224600 Number of (n+2)X4 0..2 matrices with each 3X3 subblock idempotent 1

%I #6 Aug 22 2016 05:15:06

%S 178,272,371,449,630,894,1221,1707,2440,3476,4979,7189,10414,15114,

%T 22001,32083,46840,68452,100119,146509,214482,314086,460049,673947,

%U 987416,1446808,2120063,3106745,4552782,6672030,9777921,14329803,21000892

%N Number of (n+2)X4 0..2 matrices with each 3X3 subblock idempotent

%C Column 2 of A224606

%H R. H. Hardin, <a href="/A224600/b224600.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.: 178*x + 272*x^2 -x^3*(-371 +664*x -25*x^2 -273*x^3 +123*x^4 -384*x^5 +268*x^6) / ( (1+x)*(x^3+x-1)*(x-1)^3 ). - _R. J. Mathar_, Aug 22 2016

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 11 2013

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Last modified June 20 09:35 EDT 2024. Contains 373515 sequences. (Running on oeis4.)