|
| |
|
|
A141631
|
|
3*n^2 - 4*n + 3.
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
First bisection of A133146.
|
|
|
LINKS
|
Table of n, a(n) for n=1..47.
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
|
|
|
FORMULA
|
a(n) = A133146(2n-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, with 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
|
|
|
MATHEMATICA
|
s=2; lst={s}; Do[s+=n+5; AppendTo[lst, s], {n, 0, 6!, 6}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 04 2008 *)
Table[3 n^2 - 4 n + 3, {n, 50}] (* Harvey P. Dale, Oct 28 2012 *)
|
|
|
PROG
|
(PARI) a(n)=3*n^2-4*n+3 \\ Charles R Greathouse IV, Jun 17 2017
|
|
|
CROSSREFS
|
Cf. A000004 (third differences), A010722 (second differences).
Sequence in context: A184096 A136583 A307684 * A172188 A077131 A212685
Adjacent sequences: A141628 A141629 A141630 * A141632 A141633 A141634
|
|
|
KEYWORD
|
nonn,less,easy
|
|
|
AUTHOR
|
Paul Curtz, Aug 28 2008
|
|
|
EXTENSIONS
|
Edited and extended by R. J. Mathar, Oct 15 2008
|
|
|
STATUS
|
approved
|
| |
|
|
