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A008729 Molien series for 3-dimensional group [2, n] = *22n. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 194

Index entries for Molien series

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

FORMULA

From Mitch Harris, Sep 08 2008: (Start)

a(n) = Sum_{j=0..n+11} floor(j/11).

a(n-11) = (1/2)*floor(n/11)*(2*n - 9 - 11*floor(n/11)). (End)

a(n) = A218530(n+11). - Philippe Deléham, Apr 03 2013

From Chai Wah Wu, Jul 08 2016: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-11) - 2*a(n-12) + a(n-13) for n > 12.

G.f.: 1/(1 - 2*x + x^2 - x^11 + 2*x^12 - x^13). (End)

EXAMPLE

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

.13...15...17...19...21...23...25...27...29...31...33

.36...39...42...45...48...51...54...57...60...63...66

.70...74...78...82...86...90...94...98..102..106..110

115..120..125..130..135..140..145..150..155..160..165

171..177..183..189..195..201..207..213..219..225..231

238..245..252..259..266..273..280..287..294..301..308

316..324..332..340..348..356..364..372..380..388..396

405..414..423..432..441..450..459..468..477..486..495

505..515..525..535..545..555..565..575..585..595..605

...

The first six columns are A051865, A180223, A022268, A022269, A211013, A152740.

- Philippe Deléham, Apr 03 2013

MAPLE

g:= 1/((1-x)^2*(1-x^11)); gser:= series(g, x=0, 72); seq(coeff(gser, x, n), n=0..70); # modified by G. C. Greubel, Jul 30 2019

MATHEMATICA

CoefficientList[Series[1/((1-x)^2*(1-x^11)), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 11 2013 *)

PROG

(PARI) my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^11))) \\ G. C. Greubel, Jul 30 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^11)) )); // G. C. Greubel, Jul 30 2019

(Sage) (1/((1-x)^2*(1-x^11))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15];; for n in [14..70] do a[n]:=2*a[n-1]-a[n-2]+a[n-11]-2*a[n-12]+a[n-13]; od; a; # G. C. Greubel, Jul 30 2019

CROSSREFS

Cf. A001840, A001972, A008724-A008728, A008732, A218530.

Sequence in context: A033063 A032516 A218530 * A101373 A107062 A178538

Adjacent sequences:  A008726 A008727 A008728 * A008730 A008731 A008732

KEYWORD

nonn,tabf,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

STATUS

approved

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Last modified October 19 21:01 EDT 2019. Contains 328225 sequences. (Running on oeis4.)