|
%I #20 Jul 08 2023 16:28:35
%S 4,25,136,481,1300,2929,5800,10441,17476,27625,41704,60625,85396,
%T 117121,157000,206329,266500,339001,425416,527425,646804,785425,
%U 945256,1128361,1336900,1573129,1839400,2138161,2471956,2843425,3255304,3710425
%N a(n) = 4*n^4 + 17*n^2 + 4.
%C a(n) = A087475(n)*A053755(n).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (2*(n^2 - 1))^2 + (5*n)^2.
%F G.f.: (-4-25*x^4-11*x^3-51*x^2-5*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
%F E.g.f.: exp(x)*(4 + 21*x + 45*x^2 + 24*x^3 + 4*x^4). - _Stefano Spezia_, Jul 08 2023
%t Table[4n^4+17n^2+4,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{4,25,136,481,1300},50] (* _Harvey P. Dale_, Nov 08 2017 *)
%o (Magma) [4*n^4+17*n^2+4: n in [0..50]]; // _Vincenzo Librandi_, Dec 27 2010
%o (PARI) a(n)=4*n^4+17*n^2+4 \\ _Charles R Greathouse IV_, Oct 21 2022
%Y Cf. A016850, A053755, A087475, A099761.
%K nonn,easy
%O 0,1
%A _Reinhard Zumkeller_, Feb 13 2009
|
