|
%I #30 Nov 19 2023 15:41:41
%S 28,299,858,1705,2840,4263,5974,7973,10260,12835,15698,18849,22288,
%T 26015,30030,34333,38924,43803,48970,54425,60168,66199,72518,79125,
%U 86020,93203,100674,108433,116480,124815,133438,142349,151548,161035
%N a(n) = 144*n^2 - 161*n + 45.
%C 576*a(n) + 1 = (288*n - 161)^2. - _Vincenzo Librandi_, Feb 09 2012
%H Vincenzo Librandi, <a href="/A156711/b156711.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*(-28 - 215*x - 45*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{28,299,858},40]
%t Table[144n^2-161n+45,{n,50}] (* _Harvey P. Dale_, Nov 19 2023 *)
%o (Magma) I:=[28, 299, 858]; [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)=144*n^2-161*n+45 \\ _Charles R Greathouse IV_, Dec 23 2011
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 15 2009
|
