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A008815
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Expansion of (1+x^8)/((1-x)^2*(1-x^8)).
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11
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1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 17, 20, 23, 26, 29, 32, 37, 42, 47, 52, 57, 62, 67, 72, 79, 86, 93, 100, 107, 114, 121, 128, 137, 146, 155, 164, 173, 182, 191, 200, 211, 222, 233, 244, 255, 266, 277, 288, 301, 314, 327, 340, 353, 366, 379, 392, 407, 422
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1).
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FORMULA
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G.f.: (1 + x^8)/((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x^4)).
a(n) = floor( (n*(n+2) + 14 + 4*((n mod 4) - 1)*(-1)^floor(n/4))/8 ). - Tani Akinari, Jul 25 2013
a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10). - Vincenzo Librandi, May 14 2019
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MAPLE
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seq(coeff(series((1+x^8)/((1-x)^2*(1-x^8)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Sep 12 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^8)/(1-x)^2/(1-x^8), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 11, 14}, 50] (* Harvey P. Dale, Dec 17 2016 *)
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PROG
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(PARI) a(n)=(n*(n+2)+14+4*(n%4-1)*(-1)^(n\4))\8 \\ Tani Akinari, Jul 25 2013
(Magma) I:=[1, 2, 3, 4, 5, 6, 7, 8, 11, 14]; [n le 10 select I[n] else 2*Self(n-1) -Self(n-2)+Self(n-8)-2*Self(n-9)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, May 14 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^8)/((1-x)^2*(1-x^8))).list()
(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 11, 14];; for n in [11..50] do a[n]:=2*a[n-1] -a[n-2]+a[n-8]-2*a[n-9]+a[n-10]; od; a; # G. C. Greubel, Sep 12 2019
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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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