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, 162174, 171983, 182080, 192465, 203138

Offset: 1

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

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).

Crossrefs

Cf. A156711.

Programs

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]];

Mathematica

LinearRecurrence[{3,-3,1},{45,350,943},40]

PARI

a(n)=144*n^2-127*n+28 \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(45 + 215*x + 28*x^2)/(1-x)^3.

576*a(n) + 1 = (288*n - 127)^2. - Vincenzo Librandi, Feb 09 2012

From Elmo R. Oliveira, Nov 13 2024: (Start)

E.g.f.: exp(x)*(144*x^2 + 17*x + 28) - 28.

a(n) = (9*n - 4)*(16*n - 7). (End)