A108983 Inverse binomial transform of A003950.

1, 7, 41, 247, 1481, 8887, 53321, 319927, 1919561, 11517367, 69104201, 414625207, 2487751241, 14926507447, 89559044681, 537354268087, 3224125608521, 19344753651127, 116068521906761, 696411131440567, 4178466788643401

Offset: 0

Author

Philippe Deléham, Jul 23 2005

Keywords

• nonn

Comments

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]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• J. East and R. D. Gray, Idempotent generators in finite partition monoids and related semigroups, arXiv:1404.2359 [math.GR], 2014-2016.
• Index entries for linear recurrences with constant coefficients, signature (5,6).

Crossrefs

Cf. A003950.

Programs

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

Maple

seq(-((-1)^n-8*6^n)/7, n=0..100); # Robert Israel, Aug 27 2014

Mathematica

CoefficientList[Series[-(1 + 2 x)/((1 + x) (6 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 27 2014 *)

Formula

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

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

O.g.f.: -(1+2x)/[(1+x)(6x-1)]. - R. J. Mathar, Apr 02 2008

Extensions

More terms from R. J. Mathar, Apr 02 2008