A037241 - OEIS

A037241

Expansion of (1+3*x^2+7*x^3+15*x^4+13*x^5+15*x^6+8*x^7+4*x^8)/((1-x)*(1-x^2)^3*(1-x^3)^2).

1, 1, 7, 16, 46, 92, 197, 346, 616, 989, 1575, 2352, 3483, 4928, 6912, 9390, 12642, 16617, 21676, 27742, 35266, 44164, 54964, 67574, 82631, 100009, 120463, 143858, 171048, 201888, 237369, 277304, 322830, 373749, 431319, 495330, 567205, 646684

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OFFSET

0,3

COMMENTS

In the paper by Jarić and Birman, this is said to be the Molien series for the irreducible representation *X3 of the space group O_h^3-Pm3n (must be Pm-3n in the modern notation). However, in the erratum the authors clarify that it was wrong and the correct sequence for *X3 is A037243.

LINKS

Table of n, a(n) for n=0..37.

Marko V. Jarić and Joseph L. Birman, Calculation of the Molien generating function for invariants of space groups, J. Math. Phys. 18 (1977), pp. 1459-1465; Erratum on p. 2085.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-5,-3,6,6,-3,-5,-1,3,1,-1).

MATHEMATICA

LinearRecurrence[{1, 3, -1, -5, -3, 6, 6, -3, -5, -1, 3, 1, -1}, {1, 1, 7, 16, 46, 92, 197, 346, 616, 989, 1575, 2352, 3483}, 38]

(* Ray Chandler, Jul 15 2015 *)

CROSSREFS

Cf. A037243.

Sequence in context: A055553 A066009 A304013 * A154141 A173661 A152530

Adjacent sequences: A037238 A037239 A037240 * A037242 A037243 A037244