A177058 a(n) = n^3 - 3n^2 + 3.

3, 1, -1, 3, 19, 53, 111, 199, 323, 489, 703, 971, 1299, 1693, 2159, 2703, 3331, 4049, 4863, 5779, 6803, 7941, 9199, 10583, 12099, 13753, 15551, 17499, 19603, 21869, 24303, 26911, 29699, 32673, 35839, 39203, 42771, 46549, 50543, 54759, 59203

Offset: 0

Author

Vincenzo Librandi, May 27 2010

Keywords

• sign
• easy

Comments

For n>2, fourth diagonal of A162611.

Links

• B. Berselli, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A162611, A081438.

Programs

Mathematica

Table[n^3-3n^2+3,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{3,1,-1,3},50] (* Harvey P. Dale, May 15 2020 *)

PARI

a(n)=n^3-3*n^2+3 \\ Charles R Greathouse IV, Jan 11 2012

Formula

From Bruno Berselli, Jun 04 2010: (Start)

G.f.: (3-11*x+13*x^2+x^3)/(1-x)^4.

a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0, with n>3.

a(n)+a(n-1) = 2*A081438(n-3), with n>2. (End)

G.f.: 3+x+x^2*G(0) where G(k) = 1 - x*(k+1)*(k+1)*(k+4)/(1 - 1/(1 - (k+1)*(k+1)*(k+4)/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 16 2012