login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A019525 Poincaré series [or Poincare series] for depths of roots in a certain root system. 1
2, 3, 6, 12, 27, 60, 138, 315, 726, 1668, 3843, 8844, 20370, 46899, 108006, 248700, 572715, 1318812, 3036954, 6993387, 16104246, 37084404, 85397139, 196650348, 452841762, 1042792803, 2401318086, 5529696492, 12733650747, 29322740220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Posting to sci.math.research by dima(AT)win.tue.nl (Dmitrii V. Pasechnik), Oct 28 1996.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

D. Pasechnik, Poincare series for the depths of roots in a root system, Sci. Math. Research posting Oct 28 1996.

Index entries for linear recurrences with constant coefficients, signature (2,2,-3).

FORMULA

a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3).

G.f.: -x*(4*x^2+x-2) / ((x-1)*(3*x^2+x-1)). - Colin Barker, Sep 27 2013

a(n) = (78 + (13-5*sqrt(13))*((1-sqrt(13))/2)^n + ((1+sqrt(13))/2)^n*(13+5*sqrt(13))) / 78. - Colin Barker, Aug 03 2017

MATHEMATICA

CoefficientList[Series[-(4 x^2 + x - 2)/((x - 1) (3 x^2 + x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 27 2013 *)

LinearRecurrence[{2, 2, -3}, {2, 3, 6}, 30] (* Harvey P. Dale, Nov 28 2014 *)

PROG

(PARI) Vec(-x*(4*x^2+x-2)/((x-1)*(3*x^2+x-1)) + O(x^100)) \\ Colin Barker, Sep 27 2013

CROSSREFS

Sequence in context: A001677 A024422 A186771 * A108915 A082395 A061343

Adjacent sequences:  A019522 A019523 A019524 * A019526 A019527 A019528

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)