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 A014986 a(n) = (1 - (-5)^n)/6. 13
 1, -4, 21, -104, 521, -2604, 13021, -65104, 325521, -1627604, 8138021, -40690104, 203450521, -1017252604, 5086263021, -25431315104, 127156575521, -635782877604, 3178914388021, -15894571940104, 79472859700521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS q-integers for q = -5. Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-5, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 27 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (-4,5). FORMULA a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1). G.f.: x/((1-x)*(1+5*x)). - Bruno Berselli, Dec 07 2011 a(n) = -4*a(n-1) + 5*a(n-2). - Vincenzo Librandi, Jun 19 2012 E.g.f.: (exp(x) - exp(-5*x))/6. - G. C. Greubel, May 26 2018 MAPLE a:=n->sum ((-5)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008 MATHEMATICA LinearRecurrence[{-4, 5}, {1, -4}, 30] (* Vincenzo Librandi, Jun 19 2012 *) PROG (Sage) [gaussian_binomial(n, 1, -5) for n in range(1, 22)] # Zerinvary Lajos, May 28 2009 (PARI) a(n)=(1-(-5)^n)/6 \\ Charles R Greathouse IV, Dec 07 2011 (MAGMA) I:=[1, -4]; [n le 2 select I[n] else -4*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 19 2012 CROSSREFS Cf. A077925, A014983, A014985, A014987, A014989, A014990, A014991, A014992, A014993, A014994. Sequence in context: A240456 A113022 A291184 * A015531 A083425 A183367 Adjacent sequences:  A014983 A014984 A014985 * A014987 A014988 A014989 KEYWORD sign,easy AUTHOR EXTENSIONS Better name from Ralf Stephan, Jul 14 2013 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)