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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
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
Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, -1, 0, 3, -3, 0, 1, 1, 0, -2, 1).
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)).
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
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: A340775 A290436 A338048 * A185100 A103420 A329701
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 07 2007
STATUS
approved