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A127825
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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)).
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1
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1, 0, 2, 2, 4, 5, 11, 11, 20, 25, 35, 44, 63, 73, 99, 120, 150, 180, 226, 261, 320, 374, 442, 512, 605, 686, 800, 910, 1040, 1175, 1341, 1495, 1692, 1887, 2109, 2340, 2611, 2871, 3185, 3500, 3850, 4214, 4628, 5033, 5504, 5980, 6500, 7040, 7641, 8236, 8910, 9594
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OFFSET
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0,3
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COMMENTS
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The ring with this Hilbert series is not an intersection ring.
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REFERENCES
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B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, -1, 0, 3, -3, 0, 1, 1, 0, -2, 1).
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FORMULA
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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)).
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
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MATHEMATICA
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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 *)
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 *)
a[n_]:=1/864 Switch[Mod[n, 6],
0, (6+n) (144+48 n+4 n^2+n^3),
1, (-1+n) (121+83 n+11 n^2+n^3),
2, (4+n)^2 (40+2 n+n^2),
3, (1+n) (3+n) (45+6 n+n^2),
4, (2+n) (4+n) (40+4 n+n^2),
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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