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A008645
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Molien series of 6 X 6 upper triangular matrices over GF( 2 ).
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3
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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
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
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LINKS
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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).
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FORMULA
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G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)*(1-x^32)).
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/product(1-x^(2^j) for j in (0..5)) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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