A141631 a(n) = 3*n^2 - 4*n + 3.

2, 7, 18, 35, 58, 87, 122, 163, 210, 263, 322, 387, 458, 535, 618, 707, 802, 903, 1010, 1123, 1242, 1367, 1498, 1635, 1778, 1927, 2082, 2243, 2410, 2583, 2762, 2947, 3138, 3335, 3538, 3747, 3962, 4183, 4410, 4643, 4882, 5127, 5378, 5635, 5898, 6167, 6442

Offset: 1

Author

Paul Curtz, Aug 28 2008

Keywords

• nonn
• less
• easy

Comments

First bisection of A133146.

Also first bisection of A271713. - Bruno Berselli, Mar 19 2021

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000004 (third differences), A010722 (second differences).

Cf. A000290, A016969, A067998, A133146, A271713.

Programs

Mathematica

Table[3 n^2 - 4 n + 3, {n, 50}] (* Harvey P. Dale, Oct 28 2012 *)

PARI

a(n)=3*n^2-4*n+3 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = A133146(2*n-2) = (n - 2)^2 + (n - 1)*(n + 1) + n^2.

First differences: a(n+1) - a(n) = A016969(n-1).

G.f.: x*(2 + x + 3*x^2)/(1 - x)^3. - R. J. Mathar, Oct 15 2008

a(n) = 6*n + a(n-1) - 7 for n > 1, a(1)=2. - Vincenzo Librandi, Nov 25 2010

a(n) = 2*A000290(n)^2 + A067998(n-1) = 2*n^2 + (n - 1)*(n - 3). - L. Edson Jeffery, Nov 30 2013

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

E.g.f.: exp(x)*(3*x^2 - x + 3) - 3.

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

Extensions

Edited and extended by R. J. Mathar, Oct 15 2008