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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A190991 a(n) = 13*n + 1. 10 1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144, 157, 170, 183, 196, 209, 222, 235, 248, 261, 274, 287, 300, 313, 326, 339, 352, 365, 378, 391, 404, 417, 430, 443, 456, 469, 482, 495, 508, 521, 534, 547, 560, 573, 586, 599, 612, 625, 638, 651, 664, 677 (list; graph; refs; listen; history; text; internal format) OFFSET 0,2 COMMENTS Partial sums give A051867. - Leo Tavares, Mar 19 2023 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 11 2011 From Alejandro J. Becerra Jr., Jun 04 2020: (Start) a(n) = 13*A001477(n) + A000012(n). G.f.: (1 + 12*x)/(1 - x)^2. (End) E.g.f.: (1+13*x)*exp(x). - G. C. Greubel, Sep 16 2022 MATHEMATICA Range[1, 1000, 13] LinearRecurrence[{2, -1}, {1, 14}, 60] (* Harvey P. Dale, Apr 05 2014 *) PROG (Magma) [13*n + 1: n in [0..60]]; // Vincenzo Librandi, Jun 11 2011 (PARI) a(n)=13*n+1 \\ Charles R Greathouse IV, Jun 04 2020 (SageMath) [13*n+1 for n in (0..60)] # G. C. Greubel, Sep 16 2022 CROSSREFS Cf. A000012, A001477, A008594, A008595, A153080. Cf. A051867. Sequence in context: A372008 A063799 A086451 * A306985 A293183 A370119 Adjacent sequences: A190988 A190989 A190990 * A190992 A190993 A190994 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, May 29 2011 STATUS approved

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