A051461 Molien series for group G_{1,3} of order 2304.

1, 0, 1, 15, 37, 78, 229, 419, 721, 1341, 2152, 3214, 5083, 7324, 10167, 14485, 19637, 25772, 34575, 44663, 56511, 72419, 90552, 111188, 138093, 168064, 201909, 244403, 291549, 343794, 408225, 478659, 556325, 649809, 751696, 862642, 994583, 1136908, 1291355, 1471945

Offset

0,4

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,-2,-2,3,-1,-1,-3,4,4,-3,-1,-1,3,-2,-2,1,1,1,-1).

Index entries for Molien series

E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

Formula

G.f.: (x^18 + 4*x^17 + 19*x^16 + 30*x^15 + 47*x^14 + 97*x^13 + 128*x^12 + 113*x^11 + 186*x^10 + 161*x^9 + 97*x^8 + 108*x^7 + 98*x^6 + 27*x^5 + 23*x^4 + 13*x^3 - x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + x + 1)^4*(x^2 - x + 1)^2).

a(n) ~ 2*n^5/135. - Stefano Spezia, Aug 21 2022

Mathematica

CoefficientList[Series[(x^18+4x^17+19x^16+30x^15+47x^14+97x^13+ 128x^12+ 113x^11+ 186x^10+161x^9+97x^8+108x^7+ 98x^6+27x^5+23x^4+13x^3-x+1)/ ((x-1)^6(x+1)^3(x^2+x+1)^4(x^2-x+1)^2), {x, 0, 40}], x] (* Harvey P. Dale, Jan 28 2015 *)

Crossrefs

Cf. A051462, A051463.

Sequence in context: A082112 A059605 A147221 * A321383 A039605 A032654

Adjacent sequences: A051458 A051459 A051460 * A051462 A051463 A051464

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001

Status

approved