A156711 a(n) = 144*n^2 - 161*n + 45.

28, 299, 858, 1705, 2840, 4263, 5974, 7973, 10260, 12835, 15698, 18849, 22288, 26015, 30030, 34333, 38924, 43803, 48970, 54425, 60168, 66199, 72518, 79125, 86020, 93203, 100674, 108433, 116480, 124815, 133438, 142349, 151548, 161035, 170810, 180873, 191224, 201863

Offset: 1

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Magma

I:=[28, 299, 858]; [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},{28,299,858},40]
Table[144n^2-161n+45,{n,50}] (* Harvey P. Dale, Nov 19 2023 *)

PARI

a(n)=144*n^2-161*n+45 \\ Charles R Greathouse IV, Dec 23 2011

Formula

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

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

576*a(n) + 1 = (288*n - 161)^2. - Vincenzo Librandi, Feb 09 2012

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(144*x^2 - 17*x + 45) - 45.

a(n) = (9*n - 5)*(16*n - 9). (End)