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A008739
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Molien series for 3-dimensional group [2+,n] = 2*(n/2).
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1
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1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 22, 26, 30, 34, 39, 44, 49, 54, 60, 66, 72, 79, 86, 93, 100, 108, 116, 124, 133, 142, 151, 160, 170, 180, 190, 201, 212, 223, 234, 246, 258, 270, 283, 296, 309, 322, 336, 350, 364, 379, 394, 409, 424, 440, 456, 472, 489
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1+x^4)/((1-x)^2*(1-x^7)).
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MATHEMATICA
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LinearRecurrence[{2, -1, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 6, 8, 10, 13, 16}, 50] (* Harvey P. Dale, May 05 2017 *)
CoefficientList[Series[(1+x^4)/(1-x)^2/(1-x^7), {x, 0, 50}], x] (* Vincenzo Librandi, May 06 2017 *)
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PROG
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(Magma) I:=[1, 2, 3, 4, 6, 8, 10, 13, 16]; [n le 9 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-7)-2*Self(n-8)+Self(n-9): n in [1..50]]; // Vincenzo Librandi, May 06 2017
(PARI) my(x='x+O('x^50)); Vec((1+x^4)/((1-x)^2*(1-x^7))) \\ G. C. Greubel, Aug 03 2019
(Sage) ((1+x^4)/((1-x)^2*(1-x^7))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 03 2019
(GAP) a:=[1, 2, 3, 4, 6, 8, 10, 13, 16];; for n in [10..50] do a[n]:=2*a[n-1] -a[n-2]+a[n-7]-2*a[n-8]+a[n-9]; od; a; # G. C. Greubel, Aug 03 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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