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A141530 a(n) = 4*n^3 - 6*n^2 + 1.

%I A141530 #41 Mar 12 2024 02:32:49
%S A141530 1,-1,9,55,161,351,649,1079,1665,2431,3401,4599,6049,7775,9801,12151,
%T A141530 14849,17919,21385,25271,29601,34399,39689,45495,51841,58751,66249,
%U A141530 74359,83105,92511,102601,113399,124929,137215,150281,164151,178849,194399,210825,228151
%N A141530 a(n) = 4*n^3 - 6*n^2 + 1.
%H A141530 G. C. Greubel, <a href="/A141530/b141530.txt">Table of n, a(n) for n = 0..500</a>
%H A141530 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A141530 a(n) = (2*n-1)*(2*n^2 - 2*n - 1) = A060747(n)*A132209(n-1), n > 1. - _R. J. Mathar_, Feb 22 2009
%F A141530 G.f.: (1 - 5*x + 19*x^2 + 9*x^3)/(1-x)^4. - _Jaume Oliver Lafont_, Aug 30 2009
%F A141530 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1, a(1)=-1, a(2)=9, a(3)=55. - _Harvey P. Dale_, Nov 30 2011
%F A141530 E.g.f.: (1 - 2*x + 6*x^2 + 4*x^3)*exp(x). - _G. C. Greubel_, Mar 29 2021
%p A141530 A141530:= n-> 4*n^3 -6*n^2 +1; seq(A141530(n), n=0..50); # _G. C. Greubel_, Mar 29 2021
%t A141530 Array[4*#^3-6*#^2+1&,50,0] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t A141530 LinearRecurrence[{4,-6,4,-1},{1,-1,9,55},50] (* _Harvey P. Dale_, Nov 30 2011 *)
%o A141530 (PARI) a(n)=4*n^3-6*n^2+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A141530 (Magma) [4*n^3 -6*n^2 +1: n in [0..50]]; // _G. C. Greubel_, Mar 29 2021
%o A141530 (Sage) [4*n^3 -6*n^2 +1 for n in (0..50)] # _G. C. Greubel_, Mar 29 2021
%o A141530 (Python)
%o A141530 def A141530(n): return (m:=(n<<1)-1)*(n*(m-1)-1) # _Chai Wah Wu_, Mar 11 2024
%Y A141530 Cf. A046092, A141047, A141417.
%Y A141530 See Librandi's comment in A078371.
%K A141530 sign,less,easy
%O A141530 0,3
%A A141530 _Paul Curtz_, Aug 12 2008
%E A141530 Corrected, completed and edited, following an observation from _Vincenzo Librandi_, by _M. F. Hasler_, Feb 12 2009
%E A141530 Further edited by _N. J. A. Sloane_, Feb 13 2009