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A008730 Molien series 1/((1-x)^2*(1-x^12)) for 3-dimensional group [2,n] = *22n. 2

%I

%S 1,2,3,4,5,6,7,8,9,10,11,12,14,16,18,20,22,24,26,28,30,32,34,36,39,42,

%T 45,48,51,54,57,60,63,66,69,72,76,80,84,88,92,96,100,104,108,112,116,

%U 120,125,130,135,140,145,150,155,160,165,170,175,180,186,192,198,204

%N Molien series 1/((1-x)^2*(1-x^12)) for 3-dimensional group [2,n] = *22n.

%H Vincenzo Librandi, <a href="/A008730/b008730.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=195">Encyclopedia of Combinatorial Structures 195</a>

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

%F From _Mitch Harris_, Sep 08 2008: (Start)

%F a(n) = Sum_{j=0..n+12} floor(j/12).

%F a(n-12) = (1/2)*floor(n/12)*(2*n - 10 - 12*floor(n/12)). (End)

%F a(n) = A221912(n+12). - _Philippe Deléham_, Apr 03 2013

%e ..1....2....3....4....5....6....7....8....9...10...11...12

%e .14...16...18...20...22...24...26...28...30...32...34...36

%e .39...42...45...48...51...54...57...60...63...66...69...72

%e .76...80...84...88...92...96..100..104..108..112..116..120

%e 125..130..135..140..145..150..155..160..165..170..175..180

%e 186..192..198..204..210..216..222..228..234..240..246..252

%e 259..266..273..280..287..294..301..308..315..322..329..336

%e 344..352..360..368..376..384..392..400..408..416..424..432

%e 441..450..459..468..477..486..495..504..513..522..531..540

%e 550..560..570..580..590..600..610..620..630..640..650..660

%e ...

%e The columns are: A051866, A139267, A094159, A033579, A049452, A033581, A049453, A033580, A195319, A202804, A211014, A049598

%e - _Philippe Deléham_, Apr 03 2013

%p seq(coeff(series(1/(1-x)^2/(1-x^12), x, n+1), x, n), n=0..80);

%t CoefficientList[Series[1/((1-x)^2*(1-x^12)), {x,0,70}], x] (* _Vincenzo Librandi_, Jun 11 2013 *)

%o (PARI) my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^12))) \\ _G. C. Greubel_, Jul 30 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^12)) )); // _G. C. Greubel_, Jul 30 2019

%o (Sage) (1/((1-x)^2*(1-x^12))).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 30 2019

%Y Cf. A001840, A001972, A008724, A008725, A008726, A008727, A008728, A008729, A008732. - _Vladimir Joseph Stephan Orlovsky_, Mar 14 2010

%Y Cf. A221912

%K nonn,tabf,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 14 2010

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)