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 A014994 a(n) = (1 - (-12)^n)/13. 13
 1, -11, 133, -1595, 19141, -229691, 2756293, -33075515, 396906181, -4762874171, 57154490053, -685853880635, 8230246567621, -98762958811451, 1185155505737413, -14221866068848955, 170662392826187461 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS q-integers for q=-12. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..900 Index entries for linear recurrences with constant coefficients, signature (-11,12). FORMULA a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1). G.f.: x/((1 - x)*(1 + 12*x)). - Vincenzo Librandi, Oct 22 2012 a(n) = -11*a(n-1) + 12*a(n-2). - Vincenzo Librandi, Oct 22 2012 E.g.f.: (exp(x) - exp(-12*x))/13. - G. C. Greubel, May 26 2018 MAPLE a:=n->sum ((-12)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008 MATHEMATICA LinearRecurrence[{-11, 12}, {1, -11}, 30] (* Vincenzo Librandi, Oct 22 2012 *) PROG (Sage) [gaussian_binomial(n, 1, -12) for n in xrange(1, 18)] # Zerinvary Lajos, May 28 2009 (MAGMA) I:=[1, -11]; [n le 2 select I[n] else -11*Self(n-1)+12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012 (PARI) a(n)=(1-(-12)^n)/13 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A077925, A014983, A014985-A014987, A014989-A014993. Sequence in context: A196731 A289415 A051431 * A015609 A250460 A157773 Adjacent sequences:  A014991 A014992 A014993 * A014995 A014996 A014997 KEYWORD sign,easy AUTHOR EXTENSIONS Better name from Ralf Stephan, Jul 14 2013 STATUS approved

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Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)