|
|
A008652
|
|
Molien series for group of 3 X 3 upper triangular matrices over GF( 4 ).
|
|
2
|
|
|
1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10, 12, 12, 12, 12, 15, 15, 15, 15, 18, 18, 18, 18, 21, 21, 21, 21, 24, 24, 24, 24, 28, 28, 28, 28, 32, 32, 32, 32, 36, 36, 36, 36, 40, 40
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Partitions into parts 1, 4, and 16. - Joerg Arndt, Apr 29 2014
|
|
REFERENCES
|
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1).
|
|
FORMULA
|
G.f.: 1/((1-x)*(1-x^4)*(1-x^16)).
G.f.: 1/((1+x)^2*(1-x)^3*(1+x^2)^2*(1+x^4)*(1+x^8)). - Bruno Berselli, Jul 25 2013
|
|
MAPLE
|
seq(coeff(series(1/((1-x)*(1-x^4)*(1-x^16)), x, n+1), x, n), n = 0..65); # G. C. Greubel, Sep 07 2019
|
|
MATHEMATICA
|
Table[Floor[(Floor[n/4] + 3)^2/8], {n, 0, 61}] (* or *) Table[Floor[(n + 3)^2/8], {n, 0, 15}, {4}] // Flatten (* Jean-François Alcover, Jul 17 2013, updated Feb 26 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1}, {1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 6, 6, 6, 6, 8}, 70] (* Harvey P. Dale, Jan 30 2018 *)
|
|
PROG
|
(Magma) [Floor((Floor(n/4)+3)^2/8): n in [0..65]]; // G. C. Greubel, Sep 07 2019
(Sage) [floor((floor(n/4)+3)^2/8) for n in (0..65)] # G. C. Greubel, Sep 07 2019
(GAP) List([0..65], n-> Int((Int(n/4)+3)^2/8) ); # G. C. Greubel, Sep 07 2019~
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|