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 A132209 a(0) = 0 and a(n) = 2*n^2 + 2*n - 1, for n>=1. 9
 0, 3, 11, 23, 39, 59, 83, 111, 143, 179, 219, 263, 311, 363, 419, 479, 543, 611, 683, 759, 839, 923, 1011, 1103, 1199, 1299, 1403, 1511, 1623, 1739, 1859, 1983, 2111, 2243, 2379, 2519, 2663, 2811, 2963, 3119, 3279, 3443, 3611, 3783, 3959, 4139, 4323, 4511 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially identical to A142463. Previous name was: Sequence gives X values that satisfy the integer equation 2*X^3 + 3*X^2 = Y^2. To find Y values: b(n) = (2*n^2 + 2*n - 1)*(2*n - 1). LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 FORMULA a(n) = 2*n^2 + 2*n - 1 for n>=1. G.f.: x*(1+x)*(3-x)/(1-x)^3. - R. J. Mathar, Nov 14 2007 E.g.f.: 1 + (2*x^2 + 4*x -1)*exp(x). - G. C. Greubel, Jul 13 2017 MATHEMATICA f[n_]:=Inner[Times, {n, n+1}, {n+2, n+3}, Plus]; Table[f[n], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *) Join[{0}, LinearRecurrence[{3, -3, 1}, {3, 11, 23}, 40]] (* Vincenzo Librandi, Sep 22 2015 *) PROG (MAGMA) [0] cat [2*n^2+2*n-1: n in [1..50]]; // Vincenzo Librandi, Sep 22 2015 (PARI) for(n=0, 50, print1(if(n==0, 0, 2*n^2 + 2*n -1), ", ")) \\ G. C. Greubel, Jul 13 2017 CROSSREFS Cf. A005563, A046092, A001082, A002378, A036666, A062717, A028347, A087475, A000217. Cf. A153238. - Vincenzo Librandi, Jan 03 2009 Sequence in context: A072671 A119173 A106201 * A142463 A289575 A086497 Adjacent sequences:  A132206 A132207 A132208 * A132210 A132211 A132212 KEYWORD nonn AUTHOR Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007 EXTENSIONS Edited by the Associate Editors of the OEIS, Nov 15 2009 More terms from Vincenzo Librandi, Sep 22 2015 Shorter name (using formula given) from Joerg Arndt, Sep 27 2015 STATUS approved

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