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A054343 Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under action of dihedral group of the square D_4.

%I A054343 #14 May 12 2021 10:13:22
%S A054343 1,3,11,31,84,198,440,904,1766,3266,5802,9906,16384,26284,41104,62752,
%T A054343 93831,137589,198309,281249,393148,542154,738480,994320,1324668,
%U A054343 1747220,2283396,2958228,3801600,4848120,6138624,7720032,9647133,11982423,14798223,18176499
%N A054343 Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under action of dihedral group of the square D_4.
%H A054343 Colin Barker, <a href="/A054343/b054343.txt">Table of n, a(n) for n = 0..1000</a>
%H A054343 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,0,16,-24,16,8,-34,34,-8,-16,24,-16,0,8,-5,1).
%F A054343 G.f.: (2*x^6+2*x^5+x^4+4*x^2-2*x+1)/((1-x^4)^2*(1-x^2)^2*(1-x)^5).
%F A054343 a(n) = 5*a(n-1) - 8*a(n-2) + 16*a(n-4) - 24*a(n-5) + 16*a(n-6) + 8*a(n-7) - 34*a(n-8) + 34*a(n-9) - 8*a(n-10) - 16*a(n-11) + 24*a(n-12) - 16*a(n-13) + 8*a(n-15) - 5*a(n-16) + a(n-17) for n>16. - _Colin Barker_, Apr 26 2019
%e A054343 There are 11 nonisomorphic nonnegative integer 3 X 3 matrices with sum of elements equal to 2, under action of D_4:
%e A054343 [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 0] [0 0 0]
%e A054343 [0 0 0] [0 0 0] [0 0 1] [0 0 1] [0 1 0] [0 1 0] [1 0 1] [0 0 0] [0 0 0] [0 0 0] [0 2 0]
%e A054343 [0 1 1] [1 0 1] [0 1 0] [1 0 0] [0 0 1] [0 1 0] [0 0 0] [1 0 0] [0 0 2] [0 2 0] [0 0 0].
%o A054343 (PARI) Vec((2*x^6+2*x^5+x^4+4*x^2-2*x+1)/((1-x^4)^2*(1-x^2)^2*(1-x)^5) + O(x^40)) \\ _Colin Barker_, Apr 26 2019
%Y A054343 Row n=3 of A343875.
%Y A054343 Cf. A005232, A052365.
%K A054343 easy,nonn
%O A054343 0,2
%A A054343 _Vladeta Jovovic_, May 05 2000