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G.f.: (1-2*x+2*x^2-x^3+x^4-x^5+2*x^6-2*x^7+x^8)/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^6)).
1

%I #27 Jul 13 2015 22:00:09

%S 1,0,2,2,4,5,11,11,20,25,35,44,63,73,99,120,150,180,226,261,320,374,

%T 442,512,605,686,800,910,1040,1175,1341,1495,1692,1887,2109,2340,2611,

%U 2871,3185,3500,3850,4214,4628,5033,5504,5980,6500,7040,7641,8236,8910,9594

%N G.f.: (1-2*x+2*x^2-x^3+x^4-x^5+2*x^6-2*x^7+x^8)/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^6)).

%C The ring with this Hilbert series is not an intersection ring.

%D B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331.

%H Peter J. C. Moses, <a href="/A127825/b127825.txt">Table of n, a(n) for n = 0..9999</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, -1, 0, 3, -3, 0, 1, 1, 0, -2, 1).

%F Original g.f.: (1-2*t^4+2*t^8-t^12+t^16-t^20+2*t^24-2*t^28+t^32)/((1-t^4)^2*(1-t^8)*(1-t^12)*(1-t^24)).

%F a(0)=1, a(1)=0, a(2)=2, a(3)=2, a(4)=4, a(5)=5, a(6)=11, a(7)=11, a(8)=20, a(9)=25, a(10)=35, a(11)=44, a(12)=63, a(n)=2*a(n-1)-a(n-3)- a(n-4)+ 3*a(n-6)- 3*a(n-7)+ a(n-9)+a(n-10)-2*a(n-12)+a(n-13). - _Harvey P. Dale_, Feb 11 2015

%t CoefficientList[Series[(1-2*x+2*x^2-x^3+x^4-x^5+2*x^6-2*x^7+x^8)/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^6)),{x,0,50}],x] (* _Peter J. C. Moses_, Mar 26 2013 *)

%t LinearRecurrence[{2,0,-1,-1,0,3,-3,0,1,1,0,-2,1},{1,0,2,2,4,5,11,11,20,25,35,44,63},100] (* _Peter J. C. Moses_, Mar 27 2013 *)

%t a[n_]:=1/864 Switch[Mod[n,6],

%t 0,(6+n) (144+48 n+4 n^2+n^3),

%t 1,(-1+n) (121+83 n+11 n^2+n^3),

%t 2,(4+n)^2 (40+2 n+n^2),

%t 3,(1+n) (3+n) (45+6 n+n^2),

%t 4,(2+n) (4+n) (40+4 n+n^2),

%t 5,(1+n)^2 (55+8 n+n^2)] (* _Peter J. C. Moses_, Mar 28 2013 *)

%o (PARI) Vec((1-2*x+2*x^2-x^3+x^4-x^5+2*x^6-2*x^7+x^8)/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^6))+O(x^66)) /* _Joerg Arndt_, Mar 28 2013 */

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 07 2007