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A008669 Molien series for 4-dimensional complex reflection group of order 7680 (in powers of x^4). 3
1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 29, 34, 40, 47, 54, 62, 71, 80, 91, 102, 114, 127, 141, 156, 172, 189, 207, 226, 247, 268, 291, 315, 340, 367, 395, 424, 455, 487, 521, 556, 593, 631, 671, 713, 756, 801, 848, 896, 947, 999, 1053, 1109, 1167, 1227, 1289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1,2,3 and 5. - David Neil McGrath, Sep 15 2014

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,2,3,5).

L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 29).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 239

Index entries for two-way infinite sequences

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

Index entries for Molien series

FORMULA

a(n) = round((n+3)*(2*n+9)*(n+9)/360).

G.f.: 1/((1-x)(1-x^2)(1-x^3)(1-x^5)). a(n)=-a(-11-n).

a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-7)+a(n-9)+a(n-10)-a(n-11). - David Neil McGrath, Sep 15 2014

EXAMPLE

There are 6 partitions of 5 into parts 1,2,3 and 5. These are (5)(32)(311)(221)(2111)(11111). - David Neil McGrath, Sep 15 2014

MAPLE

1/(1-x)/(1-x^2)/(1-x^3)/(1-x^5)

MATHEMATICA

LinearRecurrence[{1, 1, 0, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20}, 60] (* Harvey P. Dale, Feb 25 2015 *)

PROG

(PARI) a(n)=round((n+3)*(2*n+9)*(n+9)/360)

(MAGMA) [Round((n+3)*(2*n+9)*(n+9)/360): n in [0..60]]; // Vincenzo Librandi, Jun 23 2011

CROSSREFS

Sequence in context: A049700 A002984 A109965 * A055104 A062435 A171997

Adjacent sequences:  A008666 A008667 A008668 * A008670 A008671 A008672

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 20 14:28 EST 2018. Contains 317402 sequences. (Running on oeis4.)