A008617 Expansion of 1/((1-x^2)(1-x^7)).

1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 6

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of (n+9)-digit fixed points under the base-5 Kaprekar map A165032 (see A165036 for the list of fixed points). - Joseph Myers, Sep 04 2009

It appears that this is the number of partitions of 4*n that are 8-term arithmetic progressions. Further, it seems that a(n)=[n/2]-[3n/7]. - John W. Layman, Feb 21 2012

References

• D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 214
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 0, 0, 1, 0, -1).

Programs

Mathematica

CoefficientList[Series[1 / ((1 - x^2) (1 - x^7)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 22 2013 *)
LinearRecurrence[{0,1,0,0,0,0,1,0,-1},{1,0,1,0,1,0,1,1,1},80] (* Harvey P. Dale, May 18 2018 *)

Formula

a(n) = floor((2*n+21+7*(-1)^n)/28). - Tani Akinari, May 19 2014

Extensions

Typo in name fixed by Vincenzo Librandi, Jun 22 2013