A008722 Molien series for 3-dimensional group [2,9] = *229.

1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 11, 21, 13, 23, 15, 25, 17, 27, 19, 30, 21, 33, 23, 36, 25, 39, 27, 42, 30, 45, 33, 48, 36, 51, 39, 54, 42, 58, 45, 62, 48, 66, 51, 70, 54, 74, 58, 78, 62, 82, 66, 86, 70, 90, 74, 95, 78, 100, 82

Offset

0,3

Comments

It appears that a(n) is the number of (n+11)-digit fixed points under the base-7 Kaprekar map A165071 (see A165075 for the list of fixed points). - Joseph Myers, Sep 04 2009

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 225

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1,0,0,0,0,1,0,-2,0,1).

Formula

G.f.: 1/((1-x^2)^2*(1-x^9)).

a(n) = 2*a(n-2) - a(n-4) + a(n-9) - 2*a(n-11) + a(n-13). - R. J. Mathar, Dec 18 2014

Maple

1/((1-x^2)^2*(1-x^9)); seq(coeff(series(%, x, n+1), x, n), n = 0..80); # modified by G. C. Greubel, Sep 09 2019

Mathematica

LinearRecurrence[{0, 2, 0, -1, 0, 0, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7}, 80] (* Ray Chandler, Jul 15 2015 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^9))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^9)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008722_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^2)^2*(1-x^9)) ).list()
A008722_list(80) # G. C. Greubel, Sep 09 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7];; for n in [14..80] do a[n]:= 2*a[n-2] -a[n-4]+a[n-9]-2*a[n-11]+a[n-13]; od; a; # G. C. Greubel, Sep 09 2019

Crossrefs

Sequence in context: A263397 A008803 A349375 * A008736 A263396 A029180

Adjacent sequences: A008719 A008720 A008721 * A008723 A008724 A008725

Keyword

nonn

Author

N. J. A. Sloane

Status

approved