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A008645 Molien series of 6 X 6 upper triangular matrices over GF( 2 ). 3
1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 26, 36, 36, 46, 46, 60, 60, 74, 74, 94, 94, 114, 114, 140, 140, 166, 166, 202, 202, 238, 238, 284, 284, 330, 330, 390, 390, 450, 450, 524, 524, 598, 598 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Different from A018819 (see g.f.). - Joerg Arndt, Apr 22 2016

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 245

Index entries for Molien series

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

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)*(1-x^32)).

MAPLE

seq(coeff(series( 1/mul((1-x^(2^j)), j=0..5)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Feb 02 2020

MATHEMATICA

CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^4)/(1-x^8)/(1-x^16)/(1-x^32), {x, 0, 100}], x] (* Vaclav Kotesovec, Apr 22 2016 *)

PROG

(PARI) Vec( 1/prod(j=0, 5, 1-x^(2^j)) +O('x^50) ) \\ G. C. Greubel, Feb 02 2020

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(&*[1-x^(2^j): j in [0..5]]) )); // G. C. Greubel, Feb 02 2020

(Sage)

def A008645_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( 1/product(1-x^(2^j) for j in (0..5)) ).list()

A008645_list(50) # G. C. Greubel, Feb 02 2020

CROSSREFS

Sequence in context: A184157 A008643 A008644 * A018819 A211511 A211513

Adjacent sequences:  A008642 A008643 A008644 * A008646 A008647 A008648

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 15 19:31 EDT 2021. Contains 345049 sequences. (Running on oeis4.)