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A014987 a(n) = (1 - (-6)^n)/7.

%I A014987 #41 Aug 01 2025 05:50:15
%S A014987 1,-5,31,-185,1111,-6665,39991,-239945,1439671,-8638025,51828151,
%T A014987 -310968905,1865813431,-11194880585,67169283511,-403015701065,
%U A014987 2418094206391,-14508565238345,87051391430071,-522308348580425,3133850091482551
%N A014987 a(n) = (1 - (-6)^n)/7.
%C A014987 q-integers for q=-6.
%C A014987 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-1)=(-1)^n*charpoly(A,2). - _Milan Janjic_, Jan 27 2010
%H A014987 Vincenzo Librandi, <a href="/A014987/b014987.txt">Table of n, a(n) for n = 1..200</a>
%H A014987 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-5,6).
%F A014987 a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
%F A014987 G.f.: x/((1+6*x)*(1-x)).
%F A014987 a(n) = -5*a(n-1) + 6*a(n-2). - _Vincenzo Librandi_ Oct 22 2012
%F A014987 E.g.f.: (exp(x) - exp(-6*x))/7. - _G. C. Greubel_, May 26 2018
%p A014987 a:=n->sum ((-6)^j, j=0..n): seq(a(n), n=0..25); # _Zerinvary Lajos_, Dec 16 2008
%t A014987 LinearRecurrence[{-5, 6}, {1, -5}, 30] (* _Vincenzo Librandi_ Oct 22 2012 *)
%o A014987 (Sage) [gaussian_binomial(n,1,-6) for n in range(1,22)] # _Zerinvary Lajos_, May 28 2009
%o A014987 (Magma) I:=[1,-5]; [n le 2 select I[n] else -5*Self(n-1)+6*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Oct 22 2012
%o A014987 (PARI) a(n)=(1-(-6)^n)/7 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A014987 Absolute values are in A015540.
%Y A014987 Cf. A077925, A014983, A014985, A014986, A014989-A014994.
%K A014987 sign,easy
%O A014987 1,2
%A A014987 _Olivier Gérard_
%E A014987 Better name from _Ralf Stephan_, Jul 14 2013