A108982 Inverse binomial of A003949.

1, 6, 29, 146, 729, 3646, 18229, 91146, 455729, 2278646, 11393229, 56966146, 284830729, 1424153646, 7120768229, 35603841146, 178019205729, 890096028646, 4450480143229, 22252400716146, 111262003580729, 556310017903646

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] = -3, 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

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4, 5).

Programs

GAP

List([0..25], n-> (7*5^n - (-1)^n)/6); # G. C. Greubel, Sep 25 2019

Magma

[(7*5^n - (-1)^n)/6: n in [0..25]]; // G. C. Greubel, Sep 25 2019

Maple

seq((7*5^n - (-1)^n)/6, n=0..25); # G. C. Greubel, Sep 25 2019

Mathematica

LinearRecurrence[{4,5},{1,6},30] (* Harvey P. Dale, Jul 07 2013 *)

PARI

vector(26, n, (7*5^(n-1) + (-1)^n)/6) \\ G. C. Greubel, Sep 25 2019

Sage

[(7*5^n - (-1)^n)/6 for n in (0..25)] # G. C. Greubel, Sep 25 2019

Formula

a(n) = 4*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 6.

a(2n) = 5*a(2n-1) - 1 and a(2n+1) = 5*a(2n) + 1.

From G. C. Greubel, Sep 25 2019: (Start)

G.f.: (1 + 2*x)/((1+x)*(1-5*x)).

E.g.f.: (7*exp(5*x) - exp(-x))/6. (End)

Extensions

Corrected and extended by T. D. Noe, Nov 07 2006