A013977 Molien series of 4-dimensional representation of u.g.g.r. #9.

1, 10, 40, 130, 283, 513, 883, 1372, 1994, 2836, 3853, 5059, 6565, 8302, 10284, 12646, 15295, 18245, 21655, 25408, 29518, 34168, 39217, 44679, 50761, 57298, 64304, 72010, 80227, 88969, 98491, 108580, 119250, 130780, 142933, 155723, 169453, 183862, 198964, 215086, 231943, 249549, 268255, 287752

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eiichi Bannai and Michio Ozeki, Construction of Jacobi forms from certain combinatorial polynomials, Proc. Japan Acad. A72 12-15 1996.

Manabu Oura, Molien Series Related to Certain Finite Unitary Reflection Groups, Kyushu Journal of Mathematics 50.2 (1996): 297-310. See the example of Group No. 9.

G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6, (1954), 274--304. MR0059914 (15,600b).

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Formula

G.f.: (1+8*x+21*x^2+58*x^3+47*x^4+35*x^5+21*x^6+x^7)/(1-x)^2/(1-x^3)^2.

a(n) = (32*n^3+24*n^2+27*n+9)/9 - ((2*n^2+n) mod 3)*(8*n+1)/3 - (n mod 3)*2/9. - Hoang Xuan Thanh, Apr 26 2026

Maple

(1+8*x+21*x^2+58*x^3+47*x^4+35*x^5+21*x^6+x^7)/(1-x)^2/(1-x^3)^2:
gfun[seriestolist](series(%, x, 44))[];

Mathematica

CoefficientList[Series[(1 + 8 x + 21 x^2 + 58 x^3 + 47 x^4 + 35 x^5 + 21 x^6 + x^7) / (1 - x)^2 / (1 - x^3)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Aug 15 2013 *)

Prog

(PARI) a(n)=(32/3*n^3 +8*n^2 + 19/3*n +2+if(n%3==2, -16*((n-2)/3)-12, 8*floor(n/3)+(n%3)*2+1))/3 /* Ralf Stephan, Aug 15 2013 */
(PARI) my(x='x+O('x^66)); Vec( (1+8*x+21*x^2+58*x^3+47*x^4+35*x^5+21*x^6+x^7)/(1-x)^2/(1-x^3)^2 ) \\ Joerg Arndt, Aug 15 2013

Crossrefs

Sequence in context: A199826 A227056 A027981 * A075060 A279219 A002066

Adjacent sequences: A013974 A013975 A013976 * A013978 A013979 A013980

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved