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 A067725 a(n) = 3*n^2 + 6*n. 20
 0, 9, 24, 45, 72, 105, 144, 189, 240, 297, 360, 429, 504, 585, 672, 765, 864, 969, 1080, 1197, 1320, 1449, 1584, 1725, 1872, 2025, 2184, 2349, 2520, 2697, 2880, 3069, 3264, 3465, 3672, 3885, 4104, 4329, 4560, 4797, 5040, 5289, 5544, 5805, 6072, 6345, 6624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numbers h such that 3*(3 + h) is a perfect square. - Alex Healy, Tj Tullo, Avery Pickford, Sep 20 2004 Equivalently, numbers k such that k/3+1 is a square. - Bruno Berselli, Apr 10 2018 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 3*A005563(n). - Zerinvary Lajos, Mar 06 2007 a(n) = a(n-1) + 6*n + 3, with n>0, a(0)=0. - Vincenzo Librandi, Aug 08 2010 From Colin Barker, Apr 11 2012: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: 3*x*(3-x)/(1-x)^3. (End) E.g.f.: 3*x*(x + 3)*exp(x). - G. C. Greubel, Jul 20 2017 MAPLE seq(3*n*(n+2), n=0..50); # G. C. Greubel, Sep 01 2019 MATHEMATICA Select[ Range[10000], IntegerQ[ Sqrt[ 3(3 + # )]] & ] 3*(Range[50]^2 -1) (* G. C. Greubel, Sep 01 2019 *) PROG (PARI) a(n)=3*n*(n+2) \\ Charles R Greathouse IV, Dec 07 2011 (MAGMA) [3*n*(n+2): n in [0..50]]; // G. C. Greubel, Sep 01 2019 (Sage) [3*n*(n+2) for n in (0..50)] # G. C. Greubel, Sep 01 2019 (GAP) List([0..50], n-> 3*n*(n+2)); # G. C. Greubel, Sep 01 2019 CROSSREFS Cf. A005563. Cf. numbers k such that k*(k + m) is a perfect square: A028560 (k=9), A067728 (k=8), A067727 (k=7), A067726 (k=6), A067724 (k=5), A028347 (k=4), A054000 (k=2), A005563 (k=1). Sequence in context: A063066 A262044 A097658 * A213903 A001106 A023551 Adjacent sequences:  A067722 A067723 A067724 * A067726 A067727 A067728 KEYWORD nonn,easy AUTHOR Robert G. Wilson v, Feb 05 2002 EXTENSIONS Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)