A156719 a(n) = 144*n^2 - 127*n + 28.

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

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

Sequence in context: A073873 A272850 A129153 * A228059 A155015 A179795

Adjacent sequences: A156716 A156717 A156718 * A156720 A156721 A156722

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 15 2009

Status

approved