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A008617 Expansion of 1/((1-x^2)(1-x^7)). 9

%I

%S 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,

%T 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,

%U 5,5,6,5,6,5,6,5,6,6

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

%C 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

%C 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

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

%H Vincenzo Librandi, <a href="/A008617/b008617.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=214">Encyclopedia of Combinatorial Structures 214</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 0, 0, 0, 1, 0, -1).

%F a(n) = floor((2*n+21+7*(-1)^n)/28). - _Tani Akinari_, May 19 2014

%t CoefficientList[Series[1 / ((1 - x^2) (1 - x^7)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 22 2013 *)

%t 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 *)

%K nonn,easy

%O 0,15

%A _N. J. A. Sloane_.

%E Typo in name fixed by _Vincenzo Librandi_, Jun 22 2013

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)