A108983 - OEIS

%I #33 Apr 10 2024 03:48:16

%S 1,7,41,247,1481,8887,53321,319927,1919561,11517367,69104201,

%T 414625207,2487751241,14926507447,89559044681,537354268087,

%U 3224125608521,19344753651127,116068521906761,696411131440567,4178466788643401

%N Inverse binomial transform of A003950.

%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-4, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=charpoly(A,2). [_Milan Janjic_, Jan 27 2010]

%H Vincenzo Librandi, <a href="/A108983/b108983.txt">Table of n, a(n) for n = 0..1000</a>

%H J. East and R. D. Gray, <a href="http://arxiv.org/abs/1404.2359">Idempotent generators in finite partition monoids and related semigroups</a>, arXiv:1404.2359 [math.GR], 2014-2016.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,6).

%F a(n) = 5a(n-1) + 6a(n-2), a(0) = 1, a(1) = 7.

%F a(2n) = 6a(2n-1) - 1; a(2n+1) = 6a(2n) + 1.

%F O.g.f.: -(1+2x)/[(1+x)(6x-1)]. - _R. J. Mathar_, Apr 02 2008

%p seq(-((-1)^n-8*6^n)/7, n=0..100); # _Robert Israel_, Aug 27 2014

%t CoefficientList[Series[-(1 + 2 x)/((1 + x) (6 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 27 2014 *)

%o (Magma) I:=[1,7]; [n le 2 select I[n] else 5*Self(n-1)+6*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Aug 27 2014

%Y Cf. A003950.

%K nonn

%O 0,2

%A _Philippe Deléham_, Jul 23 2005

%E More terms from _R. J. Mathar_, Apr 02 2008