A029293 - OEIS

A029293

Expansion of 1/((1-x^3)*(1-x^6)*(1-x^7)*(1-x^9)).

1, 0, 0, 1, 0, 0, 2, 1, 0, 3, 1, 0, 4, 2, 1, 5, 3, 1, 7, 4, 2, 9, 5, 3, 11, 7, 4, 14, 9, 5, 17, 11, 7, 20, 14, 9, 24, 17, 11, 28, 20, 14, 33, 24, 17, 38, 28, 20, 44, 33, 24, 50, 38, 28, 57, 44, 33, 64, 50, 38, 72, 57, 44, 81, 64

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OFFSET

0,7

COMMENTS

Number of partitions of n into parts 3, 6, 7, and 9. - Joerg Arndt, Jul 22 2014

LINKS

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

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

FORMULA

a(n) = floor((n+36)*(2*n^2+45*n+378)/13608 - ((n mod 3)*(n^2+25*n+108) + ((2*n^2+2*n) mod 3)*7*n)/324). - Hoang Xuan Thanh, Apr 02 2026

MATHEMATICA

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^7)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Jul 21 2014 *)

PROG

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^7)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

CROSSREFS

Sequence in context: A071802 A110355 A219659 * A218254 A285037 A264422

Adjacent sequences: A029290 A029291 A029292 * A029294 A029295 A029296

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved