The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A139098 a(n) = 8*n^2. 28
 0, 8, 32, 72, 128, 200, 288, 392, 512, 648, 800, 968, 1152, 1352, 1568, 1800, 2048, 2312, 2592, 2888, 3200, 3528, 3872, 4232, 4608, 5000, 5408, 5832, 6272, 6728, 7200, 7688, 8192, 8712, 9248, 9800, 10368, 10952, 11552, 12168, 12800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Opposite numbers to the centered 16-gonal numbers (A069129) in the square spiral whose vertices are the triangular numbers (A000217). 8 times the squares. - Omar E. Pol, Dec 09 2008 a(n-1) is the molecular topological index of the n-wheel graph W_n. - Eric W. Weisstein, Jul 11 2011 An n X n pandiagonal magic square has a(n) orientations. - Kausthub Gudipati, Sep 15 2011 Area of a square with diagonal 4n. - Wesley Ivan Hurt, Jun 19 2014 Sum of all the parts in the partitions of 4n into exactly two parts. - Wesley Ivan Hurt, Jul 23 2014 For n>1, a(n) is the third least number k = x + y, with x>0 and y>0, such that there are n different pairs (x,y) for which x*y/k is an integer. - Paolo P. Lava, Jan 29 2018 Equivalently: integers k such that k\$ / (k/2-1)! and k\$ / (k/2)! are both squares when A000178 (k) = k\$ = 1!*2!*...*k! is the superfactorial of k (see A348692 for further information). - Bernard Schott, Dec 02 2021 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..800 Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos. Eric Weisstein's World of Mathematics, Molecular Topological Index. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 8*A000290(n) = 4*A001105(n) = 2*A016742(n). - Omar E. Pol, Dec 13 2008 G.f.: -8*x*(1+x) / (x-1)^3. - R. J. Mathar, Nov 27 2015 From Amiram Eldar, Feb 03 2021: (Start) Sum_{n>=1} 1/a(n) = Pi^2/48 (A245058). Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/96. Product_{n>=1} (1 + 1/a(n)) = sqrt(8)*sinh(Pi/sqrt(8))/Pi. Product_{n>=1} (1 - 1/a(n)) = sqrt(8)*sin(Pi/sqrt(8))/Pi. (End) a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Wesley Ivan Hurt, Dec 03 2021 MAPLE A139098:=n->8*n^2; seq(A139098(n), n=0..50); # Wesley Ivan Hurt, Jun 19 2014 MATHEMATICA 8 Range[0, 50]^2 (* Wesley Ivan Hurt, Jun 19 2014 *) PROG (Magma) [8*n^2: n in [0..50]]; // Vincenzo Librandi, Apr 26 2011 (PARI) a(n)=8*n^2 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A000217, A000290, A016766, A033582, A069129, A001105, A016742, A245058. Cf. A348692. Subsequence of A008586 and of A349081. Sequence in context: A290960 A009245 A018842 * A224543 A211633 A130809 Adjacent sequences: A139095 A139096 A139097 * A139099 A139100 A139101 KEYWORD nonn,easy AUTHOR Omar E. Pol, Apr 25 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.

Last modified September 24 12:42 EDT 2023. Contains 365579 sequences. (Running on oeis4.)