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#22 by Alois P. Heinz at Mon Apr 03 18:31:18 EDT 2023
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#21 by Stefano Spezia at Mon Apr 03 16:17:36 EDT 2023
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#20 by Stefano Spezia at Mon Apr 03 16:16:33 EDT 2023
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<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,-1,-1)).
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#19 by Stefano Spezia at Mon Apr 03 14:43:00 EDT 2023
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E.g.f.: exp(-x)*(6 - 6*x + exp(3*x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/9. - Stefano Spezia, Apr 03 2023
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approved
editing
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#18 by Charles R Greathouse IV at Thu Sep 08 08:45:48 EDT 2022
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(MAGMAMagma) I:=[1, -1, 2, -3]; [n le 4 select I[n] else - Self(n-1)-Self(n-3)- Self(n-4): n in [1..65]]; // Vincenzo Librandi, Jul 08 2016
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Discussion
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| Thu Sep 08
| 08:45
| OEIS Server: https://oeis.org/edit/global/2944
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#17 by Alois P. Heinz at Fri Jul 08 03:31:29 EDT 2016
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#16 by Alois P. Heinz at Fri Jul 08 03:31:19 EDT 2016
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a(n) = cos(piPi*n/3)/3 + sqrt(3)*sin(piPi*n/3)/9 + 2*(n+1)*(-1)^n/3.
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| CROSSREFS
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Cf. A010892, A168051.
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reviewed
editing
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#15 by Joerg Arndt at Fri Jul 08 03:19:13 EDT 2016
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#14 by Vincenzo Librandi at Fri Jul 08 01:15:37 EDT 2016
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#13 by Vincenzo Librandi at Fri Jul 08 01:15:28 EDT 2016
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G.f.: (1+x^2)/((1+x)^2(*(1-x+x^2)).
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| MATHEMATICA
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CoefficientList[Series[(1 + x^2) / ((1 + x)^2 (1 - x + x^2)), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 08 2016 *)
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| PROG
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(MAGMA) I:=[1, -1, 2, -3]; [n le 4 select I[n] else - Self(n-1)-Self(n-3)- Self(n-4): n in [1..65]]; // Vincenzo Librandi, Jul 08 2016
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| STATUS
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proposed
editing
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