OFFSET
1,1
COMMENTS
576*a(n) + 1 = (288*n - 127)^2. - Vincenzo Librandi, Feb 09 2012
The continued fraction expansion of sqrt(a(n)) is [12n-6; {1, 2, 2, 2, 1, 24n-12}]. - Magus K. Chu, Sep 23 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).
G.f.: x*(-45 - 215*x - 28*x^2)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {45, 350, 943}, 40]
PROG
(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]];
(PARI) a(n)=144*n^2-127*n+28 \\ Charles R Greathouse IV, Dec 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 15 2009
STATUS
approved