|
%I #22 Jun 07 2023 18:31:41
%S 46,887,2786,5743,9758,14831,20962,28151,36398,45703,56066,67487,
%T 79966,93503,108098,123751,140462,158231,177058,196943,217886,239887,
%U 262946,287063,312238,338471,365762,394111,423518,453983,485506,518087
%N 529n^2 - 746n + 263.
%C The identity (279841*n^2-394634*n+139128)^2-(529*n^2-746*n+263)*(12167*n-8579)^2=1 can be written as A156844(n)^2-a(n)*A156845(n)^2=1.
%H Vincenzo Librandi, <a href="/A156842/b156842.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: x*(-46-749*x-263*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{46,887,2786},40]
%t Table[529n^2-746n+263,{n,40}] (* _Harvey P. Dale_, Jun 07 2023 *)
%o (Magma) I:=[46, 887, 2786]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n)=529*n^2-746*n+263 \\ _Charles R Greathouse IV_, Dec 23 2011
%Y Cf. AA156844, A156845, A156849.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 17 2009
%E Edited by _Charles R Greathouse IV_, Jul 25 2010
|
