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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097080 a(n) = 2*n^2 - 2*n + 3. 21
 3, 7, 15, 27, 43, 63, 87, 115, 147, 183, 223, 267, 315, 367, 423, 483, 547, 615, 687, 763, 843, 927, 1015, 1107, 1203, 1303, 1407, 1515, 1627, 1743, 1863, 1987, 2115, 2247, 2383, 2523, 2667, 2815, 2967, 3123, 3283, 3447, 3615, 3787, 3963, 4143, 4327, 4515, 4707 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The rational numbers may be totally ordered, first by height (see A002246) and then by magnitude; every rational number of height n appears in this ordering at a position <= a(n). This ordering of the rationals is given in A113136/A113137. The old entry with this sequence number was a duplicate of A027356. This is also the sum of the pairwise averages of five consecutive triangular numbers in A000217. Start with A000217(0): (0+1)/2 + (1+3)/2 + (3+6)/2 + (6+10)/2 = 15, which is the third term of this sequence. Simply continue to create this sequence. - J. M. Bergot, Jun 13 2012 2*a(n) is inverse radius (curvature) of the touching circle of the large semicircle (radius 1) and the n-th and (n-1)-st circles of the Pappus chain of the symmetric Arbelos. One can use Descartes three circle theorem to find the solution 4*n^2 - 4*n + 6, n >= 1. Note that the circle with curvature 6 is also the third circle of the clockwise Pappus chain, which is A059100(2) (by symmetry). See the illustration. - Wolfdieter Lang and Kival Ngaokrajang, Jul 01 2015 Numbers k such that 2*k - 5 is a square. - Bruno Berselli, Nov 08 2017 REFERENCES Steven Edwards and W. Griffiths, Generalizations of Delannoy and cross polytope numbers, Fib. Q., 55 (2017), 356-366. M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Steven Edwards and William Griffiths, On Generalized Delannoy Numbers, J. Int. Seq., Vol. 23 (2020), Article 20.3.6. Kival Ngaokrajang, Illustration of the Pappus chain of the symmetric Arbelos Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 4*(n-1) + a(n-1) for n>1, a(1)=3. - Vincenzo Librandi, Nov 16 2010 a(n) = A046092(n) + 3. - Reinhard Zumkeller, Dec 15 2013 G.f.: x*(3 - 2*x + 3*x^2)/(1 - x)^3. - Vincenzo Librandi, Aug 03 2014 a(n) = A027575(n-2)/2. - Michel Marcus, Nov 11 2015 MATHEMATICA Table[2n^2-2n+3, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {3, 7, 15}, 50] (* Harvey P. Dale, Aug 02 2014 *) CoefficientList[Series[(3 - 2 x + 3 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 03 2014 *) PROG (PARI) a(n)=2*n^2-2*n+3 \\ Charles R Greathouse IV, Jun 13 2012 (PARI) Vec(x*(3-2*x+3*x^2)/(1-x)^3 + O(x^50)) \\ Altug Alkan, Nov 11 2015 (Haskell) a097080 n = 2 * n * (n - 1) + 3  -- Reinhard Zumkeller, Dec 15 2013 CROSSREFS Cf. A001845, A002246, A059100, A113136, A113137. Sequence in context: A324719 A170884 A182836 * A274008 A146742 A146425 Adjacent sequences:  A097077 A097078 A097079 * A097081 A097082 A097083 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 02 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)