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, 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

Peter J. C. Moses, Table of n, a(n) for n = 0..9999

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

Adjacent sequences: A127822 A127823 A127824 * A127826 A127827 A127828

Keyword

nonn

Author

N. J. A. Sloane, Apr 07 2007

Status

approved