A002625 Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)). (Formerly M2726 N1093)

1, 3, 8, 17, 33, 58, 97, 153, 233, 342, 489, 681, 930, 1245, 1641, 2130, 2730, 3456, 4330, 5370, 6602, 8048, 9738, 11698, 13963, 16563, 19538, 22923, 26763, 31098, 35979, 41451, 47571, 54390, 61971, 70371, 79660, 89901, 101171, 113540, 127092, 141904, 158068, 175668, 194804, 215568

Offset

0,2

Comments

Number of (integer) partitions of n into 3 sorts of 1's, 2 sorts of 2's, and 1 sort of 3's. - Joerg Arndt, May 17 2013

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.

E. Fix and J. L. Hodges, Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 205

Gerzson Keri and Patric R. J. Östergård, The Number of Inequivalent (2R+3,7)R Optimal Covering Codes, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.7.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,2,2,2,-4,-1,3,-1).

Formula

a(n) = floor((n+1)*(135*(-1)^n + 6*n^4 + 144*n^3 + 1256*n^2 + 4744*n + 6785)/8640+1/2). - Tani Akinari, Oct 07 2012

Maple

A002625:=1/(z**2+z+1)/(z+1)**2/(z-1)**6; [Simon Plouffe in his 1992 dissertation.]

Mathematica

CoefficientList[Series[1/((1-x)^3*(1-x^2)^2*(1-x^3)), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
LinearRecurrence[{3, -1, -4, 2, 2, 2, -4, -1, 3, -1}, {1, 3, 8, 17, 33, 58, 97, 153, 233, 342}, 50] (* Harvey P. Dale, Sep 24 2022 *)

Prog

(PARI) Vec(1/(1-x)^3/(1-x^2)^2/(1-x^3)+O(x^99)) \\ Charles R Greathouse IV, Apr 30 2012

Crossrefs

Partial sums of A097701.

Sequence in context: A294417 A001580 A360848 * A027181 A130750 A281166

Adjacent sequences: A002622 A002623 A002624 * A002626 A002627 A002628

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved