|
%I #16 Oct 18 2022 15:26:14
%S 1,1,9,31,73,141,241,379,561,793,1081,1431,1849,2341,2913,3571,4321,
%T 5169,6121,7183,8361,9661,11089,12651,14353,16201,18201,20359,22681,
%U 25173,27841,30691,33729,36961,40393,44031,47881,51949,56241,60763,65521
%N a(n) = n^3 + (1-n)^2.
%H G. C. Greubel, <a href="/A168297/b168297.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 G.f.: (1 - 3*x + 11*x^2 - 3*x^3)/(1-x)^4. - _R. J. Mathar_, Nov 24 2009
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _G. C. Greubel_, Jul 17 2016
%t Table[n^3 + (1 - n)^2, {n, 0, 50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1, 1, 9, 31}, 50] (* _G. C. Greubel_, Jul 17 2016 *)
%o (Magma) [n^3+(1-n)^2: n in [0..40]]; // _Vincenzo Librandi_, Jul 18 2016
%o (PARI) a(n)=n^3+(n-1)^2 \\ _Charles R Greathouse IV_, Oct 18 2022
%Y Cf. A153257.
%K nonn,easy
%O 0,3
%A _Vladimir Joseph Stephan Orlovsky_, Nov 22 2009
%E Flipped/normalized the sign of n - _R. J. Mathar_, Nov 24 2009
%E Further edited by _N. J. A. Sloane_, Nov 24 2009
|
