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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
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
a(n) ~ 1/128*n^2. - Ralf Stephan, Apr 29 2014
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
(PARI) a(n)=(n\4 + 3)^2\8 \\ Charles R Greathouse IV, Feb 10 2017
(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
Sequence in context: A367329 A328301 A129253 * A195120 A259506 A305817
KEYWORD
nonn,easy,nice
STATUS
approved