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%I #43 Sep 08 2022 08:44:36
%S 1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,6,6,6,6,8,8,8,8,10,10,10,10,12,12,12,
%T 12,15,15,15,15,18,18,18,18,21,21,21,21,24,24,24,24,28,28,28,28,32,32,
%U 32,32,36,36,36,36,40,40
%N Molien series for group of 3 X 3 upper triangular matrices over GF( 4 ).
%C Partitions into parts 1, 4, and 16. - _Joerg Arndt_, Apr 29 2014
%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H Vincenzo Librandi, <a href="/A008652/b008652.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=220">Encyclopedia of Combinatorial Structures 220</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1).
%F G.f.: 1/((1-x)*(1-x^4)*(1-x^16)).
%F G.f.: 1/((1+x)^2*(1-x)^3*(1+x^2)^2*(1+x^4)*(1+x^8)). - _Bruno Berselli_, Jul 25 2013
%F a(n) ~ 1/128*n^2. - _Ralf Stephan_, Apr 29 2014
%p seq(coeff(series(1/((1-x)*(1-x^4)*(1-x^16)), x, n+1), x, n), n = 0..65); # _G. C. Greubel_, Sep 07 2019
%t Table[Floor[(Floor[n/4] + 3)^2/8], {n, 0, 61}] (* or *) Table[Floor[(n + 3)^2/8], {n, 0, 15}, {4}] // Flatten (* _Jean-François Alcover_, Jul 17 2013, updated Feb 26 2016 *)
%t LinearRecurrence[{1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1}, {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,6,6,6,6,8}, 70] (* _Harvey P. Dale_, Jan 30 2018 *)
%o (PARI) a(n)=(n\4 + 3)^2\8 \\ _Charles R Greathouse IV_, Feb 10 2017
%o (Magma) [Floor((Floor(n/4)+3)^2/8): n in [0..65]]; // _G. C. Greubel_, Sep 07 2019
%o (Sage) [floor((floor(n/4)+3)^2/8) for n in (0..65)] # _G. C. Greubel_, Sep 07 2019
%o (GAP) List([0..65], n-> Int((Int(n/4)+3)^2/8) ); # _G. C. Greubel_, Sep 07 2019~
%K nonn,easy,nice
%O 0,5
%A _N. J. A. Sloane_
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