A029122 Expansion of 1/((1-x)(1-x^7)(1-x^9)(1-x^11)).

1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 8, 8, 9, 10, 11, 12, 12, 14, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 30, 31, 33, 35, 37, 39, 41, 44, 46, 49, 51, 54, 56, 59, 62, 65, 68, 71, 75, 78, 82, 85, 89, 92, 96

Offset

0,8

Comments

Number of partitions of n into parts 1, 7, 9, and 11. [Joerg Arndt, Jul 07 2013]

Links

Table of n, a(n) for n=0..60.

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

Formula

a(n) = floor((n^3+42*n^2+525*n+3744)/4158+1/6*(1+(-1)^(n+9*floor(n/9)))*(1-floor((-9*floor(n/9)+n)/3))). - Tani Akinari, Jul 07 2013

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=2, a(8)=2, a(9)=3, a(10)=3, a(11)=4, a(12)=4, a(13)=4, a(14)=5, a(15)=5, a(16)=6, a(17)=6, a(18)=8, a(19)=8, a(20)=9, a(21)=10, a(22)=11, a(23)=12, a(24)=12, a(25)=14, a(26)=14, a(27)=16, a(n)=a(n-1)+a(n-7)-a(n-8)+ a(n-9)- a(n-10)+a(n-11)-a(n-12)-a(n-16)+a(n-17)-a(n-18)+ a(n-19)- a(n-20)+ a(n-21)+a(n-27)-a(n-28). - Harvey P. Dale, Feb 27 2015

Mathematica

CoefficientList[Series[1/((1-x)(1-x^7)(1-x^9)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 8, 8, 9, 10, 11, 12, 12, 14, 14, 16}, 80] (* Harvey P. Dale, Feb 27 2015 *)

Crossrefs

Sequence in context: A104305 A050506 A155213 * A134482 A132921 A255232

Adjacent sequences: A029119 A029120 A029121 * A029123 A029124 A029125

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved