The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A053436 a(n) = n+1 + ceiling(n/2)*(ceiling(n/2)-1)*(ceiling(n/2)+1)/6. 1
2, 3, 5, 6, 10, 11, 18, 19, 30, 31, 47, 48, 70, 71, 100, 101, 138, 139, 185, 186, 242, 243, 310, 311, 390, 391, 483, 484, 590, 591, 712, 713, 850, 851, 1005, 1006, 1178, 1179, 1370, 1371, 1582, 1583, 1815, 1816, 2070, 2071, 2348, 2349, 2650, 2651 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = n + 1 + A000292(ceiling(n/2)-2).
a(n) = a(n-1) +3 a(n-2) -3 a(n-3) -3 a(n-4) +3 a(n-5) +a(n-6) -a(n-7). - R. J. Mathar, Mar 11 2012
G.f.: x*(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3). - Colin Barker, Apr 02 2012
a(n) = (2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96. - Luce ETIENNE, Oct 22 2014
MATHEMATICA
CoefficientList[Series[(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 28 2012 *)
cn[n_]:=(Times@@(Ceiling[n/2]+{1, 0, -1}))/6+n+1; Array[cn, 50] (* or *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {2, 3, 5, 6, 10, 11, 18}, 50] (* Harvey P. Dale, Mar 27 2013 *)
PROG
(Magma) [n+1 + Ceiling(n/2)*(Ceiling(n/2)-1)*(Ceiling(n/2)+1)/6: n in [1..50]]; // Vincenzo Librandi, Apr 28 2012
(PARI) for(n=1, 30, print1((2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96, ", ")) \\ G. C. Greubel, May 26 2018
CROSSREFS
Cf. A000292.
Sequence in context: A024560 A000039 A302600 * A057546 A339514 A138587
KEYWORD
easy,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 11 2000
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 May 29 15:14 EDT 2024. Contains 372952 sequences. (Running on oeis4.)