A156719 - OEIS

%I #40 Nov 14 2024 10:07:50

%S 45,350,943,1824,2993,4450,6195,8228,10549,13158,16055,19240,22713,

%T 26474,30523,34860,39485,44398,49599,55088,60865,66930,73283,79924,

%U 86853,94070,101575,109368,117449,125818,134475,143420,152653,162174,171983,182080,192465,203138

%N a(n) = 144*n^2 - 127*n + 28.

%C The continued fraction expansion of sqrt(a(n)) is [12n-6; {1, 2, 2, 2, 1, 24n-12}]. - _Magus K. Chu_, Sep 23 2022

%H Vincenzo Librandi, <a href="/A156719/b156719.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*(45 + 215*x + 28*x^2)/(1-x)^3.

%F 576*a(n) + 1 = (288*n - 127)^2. - _Vincenzo Librandi_, Feb 09 2012

%F From _Elmo R. Oliveira_, Nov 13 2024: (Start)

%F E.g.f.: exp(x)*(144*x^2 + 17*x + 28) - 28.

%F a(n) = (9*n - 4)*(16*n - 7). (End)

%t LinearRecurrence[{3,-3,1},{45,350,943},40]

%o (Magma) I:=[45, 350, 943]; [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^2-127*n+28 \\ _Charles R Greathouse IV_, Dec 23 2011

%Y Cf. A156711.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 15 2009