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 A127825 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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The ring with this Hilbert series is not an intersection ring. REFERENCES B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331. LINKS Peter J. C. Moses, Table of n, a(n) for n = 0..9999 FORMULA 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)). MATHEMATICA 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), 5, (1+n)^2 (55+8 n+n^2)] (* Peter J. C. Moses, Mar 28 2013 *) PROG (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 */ CROSSREFS Sequence in context: A125951 A054538 A095020 * A185100 A103420 A032258 Adjacent sequences:  A127822 A127823 A127824 * A127826 A127827 A127828 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 07 2007 STATUS approved

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