A029003 - OEIS

A029003

Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^9)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 22, 25, 29, 34, 38, 43, 50, 55, 62, 70, 77, 85, 95, 103, 113, 125, 135, 147, 161, 173, 187, 203, 217, 233, 252, 268, 287, 308, 327, 348, 372, 393, 417, 444, 468, 495, 525, 552, 582, 615, 645, 678, 715, 748, 785, 825, 862, 902, 946, 986, 1030

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1, 2, 3, and 9. - Joerg Arndt, Jul 07 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

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

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9)).

a(n) = floor(2/27*(floor(n/3) + 1)*cos(2*Pi*n/3) + (2*n^3 + 45*n^2 + 290*n + 744)/648). - Tani Akinari, Jul 07 2013

MATHEMATICA

CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^3) (1 - x^9)), {x, 0, 100}], x] (* Vincenzo Librandi, Jan 22 2017 *)

LinearRecurrence[{1, 1, 0, -1, -1, 1, 0, 0, 1, -1, -1, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 22, 25, 29}, 70] (* Harvey P. Dale, Jul 17 2018 *)

PROG

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9))+O(x^66)) \\ Joerg Arndt, Jul 07 2013

(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9)))); // Vincenzo Librandi, Jan 22 2017

CROSSREFS

Sequence in context: A029004 A332728 A008752 * A339279 A034296 A075745

Adjacent sequences: A029000 A029001 A029002 * A029004 A029005 A029006

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved