login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008674 Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)). 2
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 14, 16, 19, 23, 26, 30, 35, 40, 45, 52, 58, 65, 74, 82, 91, 102, 113, 124, 138, 151, 165, 182, 198, 216, 236, 256, 277, 301, 325, 350, 379, 407, 437, 471, 504, 539, 578, 617, 658, 703, 748, 795, 847, 899, 953, 1012, 1071, 1133, 1200, 1267, 1337, 1413, 1489, 1568, 1653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of partitions of n into odd parts less than or equal 9. - Seiichi Manyama, Jun 04 2017

Number of partitions (d1,d2,...,d5) of n such that 0 <= d1/1 <= d2/2 <= ... <= d5/5. - Seiichi Manyama, Jun 04 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 244

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

MAPLE

seq(coeff(series(1/mul(1-x^(2*j+1), j=0..4), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 08 2019

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^7)(1-x^9)), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 22 2013 *)

LinearRecurrence[{1, 0, 1, -1, 1, -1, 1, -2, 2, -2, 1, -2, 2, -1, 2, -2, 2, -1, 1, -1, 1, -1, 0, -1, 1}, {1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 14, 16, 19, 23, 26, 30, 35, 40, 45, 52, 58, 65, 74}, 70] (* Harvey P. Dale, Aug 13 2016 *)

PROG

(PARI) my(x='x+O('x^70)); Vec(1/prod(j=0, 4, 1-x^(2*j+1)) ) \\ G. C. Greubel, Sep 08 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/&*[1-x^(2*j+1): j in [0..4]] )); // G. C. Greubel, Sep 08 2019

(Sage)

def A008674_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( 1/prod(1-x^(2*j+1) for j in (0..4)) ).list()

A008674_list(70) # G. C. Greubel, Sep 08 2019

CROSSREFS

Cf. A259094.

Sequence in context: A240671 A034140 A109950 * A067596 A114098 A147706

Adjacent sequences:  A008671 A008672 A008673 * A008675 A008676 A008677

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Typo in name fixed by Vincenzo Librandi, Jun 22 2013

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 April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)