A157433 - OEIS

%I #16 Sep 08 2022 08:45:42

%S 13121,15841,18817,22049,25537,29281,33281,37537,42049,46817,51841,

%T 57121,62657,68449,74497,80801,87361,94177,101249,108577,116161,

%U 124001,132097,140449,149057,157921,167041,176417,186049,195937,206081,216481

%N 128n^2 + 2336n + 10657.

%C The identity (128*n^2+2336*n+10657)^2-(4*n^2+73*n+333)*( 64*n+584)^2=1 can be written as a(n)^2-A157431(n)* A157432(n)^2=1.

%H Vincenzo Librandi, <a href="/A157433/b157433.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*(-10657*x^2-23522*x-13121)/(x-1)^3

%t LinearRecurrence[{3,-3,1},{13121,15841,18817},50]

%o (Magma) I:=[13121, 15841, 18817]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

%o (PARI) a(n)=128*n^2+2336*n+10657 \\ _Charles R Greathouse IV_, Dec 27 2011

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 01 2009