A140343 a(n)=4a(n-1)-7a(n-2)+6a(n-3)-3a(n-4), n>4.

0, 0, 0, 0, 1, 4, 9, 14, 14, 0, -41, -122, -243, -364, -364, 0, 1093, 3280, 6561, 9842, 9842, 0, -29525, -88574, -177147, -265720, -265720, 0, 797161, 2391484, 4782969, 7174454, 7174454, 0, -21523361, -64570082, -129140163, -193710244, -193710244, 0, 581130733

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 sixth differences, where, besides the generic a(n)=6a(n-1)-15a(n-2)+20a(n-3)-15a(n-4)+6a(n-5), cf. A135356, there is also a shorter recurrence. Another sequence of this kind is A134581.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-7,6,-3).

Crossrefs

Cf. A135356.

Programs

Mathematica

Join[{0},LinearRecurrence[{4,-7,6,-3},{0,0,0,1},40]] (* Harvey P. Dale, Mar 11 2015 *)

Formula

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

Extensions

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