A140342 a(n)=5a(n-1)-11a(n-2)+13a(n-3)-9a(n-4)+3a(n-5)-a(n-6).

0, 0, 0, 0, 0, 1, 5, 14, 28, 42, 42, 0, -131, -417, -924, -1652, -2380, -2380, 0, 7753, 25213, 56714, 102256, 147798, 147798, 0, -479779, -1557649, -3499720, -6305992, -9112264, -9112264, 0, 29587889, 96072133, 215873462, 388991876, 562110290, 562110290, 0

Offset: 0

Author

Paul Curtz, May 29 2008

Keywords

• sign
• easy

Comments

This is the main sequence representing the degenerate case of sequences which equal their seventh difference, where besides the generic a(n)=7a(n-1)-21(n-2)+35a(n-3)-35a(n-4)+21a(n-5)-7a(n-6)+2a(n-7), cf. A135356, there is also a shorter recurrence.

After the first four terms, every seventh term is zero. - Harvey P. Dale, Sep 20 2012

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -11, 13, -9, 3, -1).

Crossrefs

Cf. A135356, A140343.

Programs

Mathematica

LinearRecurrence[{5,-11,13,-9,3,-1},{0,0,0,0,0,1},40] (* Harvey P. Dale, Sep 20 2012 *)

Formula

O.g.f.: x^5/(1-5x+11x^2-13x^3+9x^4-3x^5+x^6). - R. J. Mathar, Jul 10 2008

Extensions

Edited and extended by R. J. Mathar, Jul 10 2008