login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A140066 a(n) = (5*n^2 - 11*n + 8)/2. 4
1, 3, 10, 22, 39, 61, 88, 120, 157, 199, 246, 298, 355, 417, 484, 556, 633, 715, 802, 894, 991, 1093, 1200, 1312, 1429, 1551, 1678, 1810, 1947, 2089, 2236, 2388, 2545, 2707, 2874, 3046, 3223, 3405, 3592, 3784, 3981, 4183, 4390, 4602, 4819, 5041, 5268, 5500 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Binomial transform of [1, 2, 5, 0, 0, 0, ...] = A020821.
LINKS
Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.
FORMULA
A007318 * [1, 2, 5, 0, 0, 0, ...].
From R. J. Mathar, May 06 2008: (Start)
a(n) = A000217(n) + 4*A000217(n-2).
O.g.f.: x*(1+4*x^2)/(1-x)^3. (End)
a(n) = (8 - 11*n + 5*n^2)/2. - Emeric Deutsch, May 07 2008
a(n) = a(n-1) + 5*n - 8 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=3, a(3)=10. - Harvey P. Dale, Jan 28 2012
EXAMPLE
a(4) = 22 = (1, 3, 3, 1) dot (1, 2, 5, 0) = (1, + 6 + 15 + 0).
MAPLE
seq((8-11*n+5*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008
MATHEMATICA
Table[(5n^2-11n+8)/2, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 3, 10}, 40] (* Harvey P. Dale, Jan 28 2012 *)
PROG
(PARI) a(n)=(5*n^2-11*n+8)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A326124 A346166 A122795 * A006503 A248851 A023554
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 03 2008
EXTENSIONS
More terms from R. J. Mathar and Emeric Deutsch, May 06 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)