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 A015000 q-integers for q=-13. 4
 1, -12, 157, -2040, 26521, -344772, 4482037, -58266480, 757464241, -9847035132, 128011456717, -1664148937320, 21633936185161, -281241170407092, 3656135215292197, -47529757798798560, 617886851384381281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (-12,13). FORMULA a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1), with q=-13. a(n) = Sum_{j=0..n-1} (-13)^j. - Zerinvary Lajos, Dec 16 2008 G.f.: x/((1 - x)*(1 + 13*x)). - Vincenzo Librandi, Oct 22 2012 a(n) = -12*a(n-1) + 13*a(n-2). - Vincenzo Librandi, Oct 22 2012 From G. C. Greubel, May 26 2018: (Start) a(n) = (1 - (-13)^n)/14. E.g.f.: (exp(x) - exp(-13*x))/14. (End) MAPLE a:=n->sum ((-13)^j, j=0..n-1): seq(a(n), n=0..20); # Zerinvary Lajos, Dec 16 2008 MATHEMATICA QBinomial[Range[20], 1, -13] (* Harvey P. Dale, May 02 2012 *) LinearRecurrence[{-12, 13}, {1, -12}, 30] (* Vincenzo Librandi, Oct 22 2012 *) PROG (Sage) [gaussian_binomial(n, 1, -13) for n in range(1, 18)] # Zerinvary Lajos, May 28 2009 (Magma) I:=[1, -12]; [n le 2 select I[n] else -12*Self(n-1)+13*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012 (PARI) for(n=1, 30, print1((1-(-13)^n)/14, ", ")) \\ G. C. Greubel, May 26 2018 CROSSREFS Cf. A077925, A014983, A014985-A014987, A014989-A014994. Sequence in context: A218839 A036276 A003130 * A220225 A213376 A269642 Adjacent sequences: A014997 A014998 A014999 * A015001 A015002 A015003 KEYWORD sign,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Jan 13 2009 at the suggestion of R. J. Mathar STATUS approved

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Last modified March 22 17:57 EDT 2023. Contains 361432 sequences. (Running on oeis4.)