login
A156719
a(n) = 144*n^2 - 127*n + 28.
1
45, 350, 943, 1824, 2993, 4450, 6195, 8228, 10549, 13158, 16055, 19240, 22713, 26474, 30523, 34860, 39485, 44398, 49599, 55088, 60865, 66930, 73283, 79924, 86853, 94070, 101575, 109368, 117449, 125818, 134475, 143420, 152653
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
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
Sequence in context: A073873 A272850 A129153 * A228059 A155015 A179795
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 15 2009
STATUS
approved