A029139 Expansion of 1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)).

1, 0, 1, 1, 2, 1, 3, 2, 4, 4, 5, 5, 8, 7, 9, 10, 12, 12, 16, 15, 19, 20, 23, 23, 29, 28, 33, 35, 39, 40, 47, 47, 53, 56, 61, 63, 72, 72, 80, 84, 91, 93, 104, 105, 115, 120, 128, 132, 145, 147, 158, 165, 175, 180, 195, 198, 212, 220, 232, 238, 256, 260, 276, 286, 300, 308

Offset

0,5

Comments

Number of partitions of n into parts 2, 3, 4, and 9. - Joerg Arndt, Aug 14 2013

Links

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

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

Formula

a(n) = floor((2*n^3 + 54*n^2 + 431*n + 2247 + 81*(n+9)*(-1)^n + 192*cos(2*Pi*n/3)*(floor(n/3)+1))/2592). - Tani Akinari, Aug 13 2013

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^4)(1-x^9)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 18 2020 *)
LinearRecurrence[{0, 1, 1, 1, -1, -1, -1, 0, 2, 0, -1, -1, -1, 1, 1, 1, 0, -1}, {1, 0, 1, 1, 2, 1, 3, 2, 4, 4, 5, 5, 8, 7, 9, 10, 12, 12}, 70] (* Harvey P. Dale, Aug 18 2024 *)

Prog

(PARI) Vec( 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^9)) + O(x^66) ) \\ Joerg Arndt, Aug 14 2013
(PARI) a(n)=round((2*n^3+54*n^2+399*n+899)/2592+(n%3==0)*n/27+(n+9)*(-1)^n/32) \\ Tani Akinari, Jun 03 2014

Crossrefs

Sequence in context: A144693 A328399 A328171 * A100927 A001687 A159072

Adjacent sequences: A029136 A029137 A029138 * A029140 A029141 A029142

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved