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A008649 Molien series of 3 X 3 upper triangular matrices over GF( 3 ). 2
1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 22, 22, 22, 26, 26, 26, 30, 30, 30, 35, 35, 35, 40, 40, 40, 45, 45, 45, 51, 51, 51, 57, 57, 57, 63, 63, 63, 70, 70, 70, 77, 77, 77, 84, 84, 84, 92, 92, 92, 100, 100, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of partitions of n into parts 1, 3 or 9. - Reinhard Zumkeller, Aug 12 2011

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

LINKS

Table of n, a(n) for n=0..68.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 219

Index entries for Molien series

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

FORMULA

G.f.: 1/((1-x)*(1-x^3)*(1-x^9)).

a(n) = floor((6*(floor(n/3)+1)*(3*floor(n/3)-n+1)+n^2+13*n+58)/54). - Tani Akinari, Jul 12 2013

MAPLE

1/((1-x)*(1-x^3)*(1-x^9)): seq(coeff(series(%, x, n+1), x, n), n=0..70);

CROSSREFS

Sequence in context: A285582 A032562 A076973 * A008650 A062051 A179269

Adjacent sequences:  A008646 A008647 A008648 * A008650 A008651 A008652

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)