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%I #32 Sep 08 2022 08:44:52
%S 1,2,17,66,169,346,617,1002,1521,2194,3041,4082,5337,6826,8569,10586,
%T 12897,15522,18481,21794,25481,29562,34057,38986,44369,50226,56577,
%U 63442,70841,78794,87321,96442,106177,116546,127569,139266,151657
%N a(n) = (10*n^3 - 9*n^2 + 2*n)/3 + 1.
%H Vincenzo Librandi, <a href="/A034721/b034721.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = A034720(n) + 1 for n > 0, where +1 counts the empty string.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 21 2012
%F G.f.: (1 - 2*x + 15x^2 + 6x^3)/(1-x)^4. - _Bruno Berselli_, Jun 21 2012
%F E.g.f.: (3 + 3*x + 21*x^2 + 10*x^3)*exp(x)/3. - _G. C. Greubel_, Nov 11 2019
%p seq((10*n^3 -9*n^2 +2*n +3)/3, n=0..40); # _G. C. Greubel_, Nov 11 2019
%t LinearRecurrence[{4,-6,4,-1},{1,2,17,66},40] (* _Vincenzo Librandi_, Jun 21 2012 *)
%o (PARI) a(n)=(10*n^3-9*n^2+2*n)/3+1 \\ _Charles R Greathouse IV_, Dec 08 2011
%o (Magma) I:=[1, 2, 17, 66]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jun 21 2012
%o (Sage) [(10*n^3 -9*n^2 +2*n +3)/3 for n in (0..40)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([0..40], n-> (10*n^3 -9*n^2 +2*n +3)/3); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A034720.
%K nonn,easy
%O 0,2
%A _Felice Russo_
%E Edited by _Frank Ellermann_, Mar 13 2002
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