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A008624 Expansion of (1+x^3)/((1-x^2)*(1-x^4)) = (1-x+x^2)/((1+x)*(1-x)^2*(1+x^2)). 6
1, 0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 7, 8, 8, 9, 8, 9, 9, 10, 9, 10, 10, 11, 10, 11, 11, 12, 11, 12, 12, 13, 12, 13, 13, 14, 13, 14, 14, 15, 14, 15, 15, 16, 15, 16, 16, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Molien series of 2-dimensional representation of group of order 16 over GF(3).

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 107.

LINKS

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

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

From Reinhard Zumkeller, Aug 05 2005: (Start)

a(n) = floor(n/4) + ((n mod 2 + 1 - floor((n mod 4)/3)) mod 2).

a(n) = A110654(A028242(n)).

(End)

a(n) = (3 + 3*(-1)^n + (1-i)*(-i)^n + (1+i)*i^n + 2*n) / 8 where i = sqrt(-1). - Colin Barker, Oct 15 2015

MAPLE

f := x -> (1+x^3)/((1-x^2)*(1-x^4)): seq(coeff(series(f(x), x, n+1), x, n), n=0..64);

a := n -> floor(n/4) + ((n mod 2 + 1 - floor((n mod 4)/3)) mod 2): seq(a(n), n=0..64); # Johannes W. Meijer, Oct 08 2013

MATHEMATICA

CoefficientList[Series[(1 + x^3) / (1 - x^2) / (1 - x^4), {x, 0, 70}], x] (* Vincenzo Librandi, Aug 15 2013 *)

PROG

(PARI) a(n) = (3 + 3*(-1)^n + (1-I)*(-I)^n + (1+I)*I^n + 2*n) / 8 \\ Colin Barker, Oct 15 2015

(PARI) x='x+O('x^100); Vec((1+x^3)/((1-x^2)*(1-x^4))) \\ Altug Alkan, Dec 24 2015

CROSSREFS

Essentially the same as A059169.

Cf. A110659.

Sequence in context: A232548 A029363 A033922 * A059169 A026922 A178696

Adjacent sequences:  A008621 A008622 A008623 * A008625 A008626 A008627

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Replaced x^2 three times with x in the generating function (un-aerated). - R. J. Mathar, Oct 23 2008

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.