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 A158057 First differences of A051870: 16*n + 1. 16
 1, 17, 33, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 513, 529, 545, 561, 577, 593, 609, 625, 641, 657, 673, 689, 705, 721, 737, 753, 769, 785, 801, 817, 833, 849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The identity (16*n+1)^2 - (16*n^2+2*n)*(4)^2 = 1 can be written as a(n+1)^2 - A158056(n)*(4)^2 = 1. - Vincenzo Librandi, Feb 09 2012 This sequence gives the 18-gonal (or octadecagonal) gnomonic numbers. Name suggested by Todd Silvestri, Nov 22 2014 All elements are odd and contains subsequence A249356. - Todd Silvestri, Nov 22 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 OEIS Wiki, Gnomonic numbers Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = 16*n + 1. a(n) = 2*a(n-1) - a(n-2), a(0) = 1, a(1) = 17. G.f.: (1+15*x)/(1-x)^2. - Vincenzo Librandi, Nov 23 2014 E.g.f.: (1 + 18*x)*exp(x). - G. C. Greubel, Sep 18 2019 MAPLE seq(16*n+1, n=0..60); # G. C. Greubel, Sep 18 2019 MATHEMATICA LinearRecurrence[{2, -1}, {1, 17}, 60] Table[16*n+1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *) a[n_Integer/; n>=0]:=16 n+1 (* Todd Silvestri, Nov 22 2014 *) CoefficientList[Series[(1+15x)/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Nov 23 2014 *) PROG (MAGMA) I:=[1, 17]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; (PARI) a(n)=n<<4+1 \\ Charles R Greathouse IV, Dec 23 2011 (Sage) [16*n+1 for n in (0..60)] # G. C. Greubel, Sep 18 2019 (GAP) List([0..60], n-> 16*n+1); # G. C. Greubel, Sep 18 2019 CROSSREFS Cf. A051870, A158056. Sequence in context: A138393 A044062 A044443 * A249356 A286679 A116523 Adjacent sequences:  A158054 A158055 A158056 * A158058 A158059 A158060 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 12 2009 EXTENSIONS Name clarified and offset changed by Todd Silvestri, Nov 22 2014 Edited by Vincenzo Librandi Nov 23 2014 Edited: Offset changed to 0 according to the Todd Silvestri proposal. Name changed. - Wolfdieter Lang, Nov 29 2014 STATUS approved

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)