A127146 Q(n,4), where Q(m,k) is defined in A127080 and A127137.

12, 3, -4, -9, -12, -13, -12, -9, -4, 3, 12, 23, 36, 51, 68, 87, 108, 131, 156, 183, 212, 243, 276, 311, 348, 387, 428, 471, 516, 563, 612, 663, 716, 771, 828, 887, 948, 1011, 1076, 1143, 1212, 1283, 1356, 1431, 1508, 1587, 1668, 1751, 1836, 1923, 2012, 2103, 2196, 2291

Offset: 0

Author

N. J. A. Sloane, Mar 24 2007

Keywords

• sign
• easy

References

• V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

A row of A127080.

Programs

GAP

List([0..60], n-> (n-5)^2 -13); # G. C. Greubel, Aug 25 2019

Magma

[(n-5)^2 -13: n in [0..60]]; // G. C. Greubel, Aug 25 2019

Maple

seq((n-5)^2 -13, n=0..60); # G. C. Greubel, Aug 25 2019

Mathematica

Table[n^2-10n+12,{n,0,60}]  (* Harvey P. Dale, Apr 02 2011 *)
Range[-5, 55]^2 - 13 (* G. C. Greubel, Aug 25 2019 *)

PARI

a(n)=n^2-10*n+12 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[lucas_number2(2,n,6-n) for n in range(-6,48)] # Zerinvary Lajos, Mar 12 2009

Formula

a(n) = n^2 - 10*n + 12.

a(n) = a(n-1) + 2*n - 11, with a(0)=12. - Vincenzo Librandi, Nov 23 2010

G.f.: (12 - 33*x + 23*x^2)/(1 - x)^3. - Harvey P. Dale, Apr 02 2011

E.g.f.: (12 - 9*x + x^2)*exp(x). - G. C. Greubel, Aug 25 2019