OFFSET
1,1
COMMENTS
The identity (10368*n^2 - 15840*n + 6049)^2 - (36*n^2 - 55*n + 21)*(1728*n - 1320)^2 = 1 can be written as A157264(n)^2 - a(n)*A157263(n)^2 = 1. - Vincenzo Librandi, Jan 27 2012
The continued fraction expansion of sqrt(a(n)) is [6n-5; {2, 2, 2, 12n-10}]. For n=1, this collapses to [1; {2}]. - Magus K. Chu, Sep 05 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012
G.f.: x*(-2-49*x-21*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012
E.g.f.: (36*x^2 - 19*x + 21)*exp(x) - 21. - G. C. Greubel, Feb 04 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {2, 55, 180}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
Table[36*n^2-55*n+21, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)
PROG
(PARI) a(n)=36*n^2-55*n+21 \\ Charles R Greathouse IV, Dec 28 2011
(Magma) I:=[2, 55, 180]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 26 2009
STATUS
approved