The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A071253 a(n) = n^2*(n^2+1). 20
 0, 2, 20, 90, 272, 650, 1332, 2450, 4160, 6642, 10100, 14762, 20880, 28730, 38612, 50850, 65792, 83810, 105300, 130682, 160400, 194922, 234740, 280370, 332352, 391250, 457652, 532170, 615440, 708122, 810900, 924482, 1049600, 1187010, 1337492, 1501850, 1680912 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The identity (n^5+n^3)^2+(n^2*(n^2+1))^2 = n*(n^3+n)^3 can be written as A155977(n)^2+a(n)^2 = n*A034262(n)^3. - Vincenzo Librandi, Aug 08 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = A002522(n)*A000290(n). - Zerinvary Lajos, Apr 20 2008 a(n) = (1/4)*sinh(2*arcsinh(n))^2. - Artur Jasinski, Feb 10 2010 G.f.: 2*x*(1+x)*(1+4*x+x^2)/(1-x)^5. - Colin Barker, Jan 08 2012 a(n) = A002378(A000290(n)). - Rick L. Shepherd, Sep 22 2014 Sum_{n>=1} 1/a(n) = 0.5682... = Pi^2/6- (Pi*coth Pi-1)/2 = A013661 - A259171 [J. Math. Anal. Appl. 316 (2006) 328]. - R. J. Mathar, Oct 18 2019 a(n) = 2*A037270(n). - R. J. Mathar, Oct 18 2019 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/12 - 1/2 + Pi*cosech(Pi)/2. - Amiram Eldar, Nov 05 2020 MAPLE with(combinat):seq(lcm(fibonacci(3, n), n^2), n=0..35); # Zerinvary Lajos, Apr 20 2008 a:=n->add(n+add(n+add(n, j=1..n-1), j=1..n), j=1..n):seq(a(n), n=0..21); # Zerinvary Lajos, Aug 27 2008 MATHEMATICA Table[(1/4) Round[N[Sinh[2 ArcSinh[n]]^2, 100]], {n, 0, 10}] (* Artur Jasinski, Feb 10 2010 *) Table[n^2*(n^2+1), {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *) CoefficientList[Series[2 x (1 + x) (1 + 4 x + x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *) PROG (PARI) a(n)=n^2*(n^2+1) \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A034262, A069187, A155977. Sequence in context: A098077 A279264 A063663 * A069187 A328510 A033840 Adjacent sequences:  A071250 A071251 A071252 * A071254 A071255 A071256 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jun 12 2002 STATUS approved

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

Last modified December 2 19:12 EST 2020. Contains 338891 sequences. (Running on oeis4.)