A029002 Expansion of 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^8)).

1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 19, 23, 26, 31, 35, 41, 46, 53, 59, 67, 74, 83, 91, 102, 111, 123, 134, 147, 159, 174, 187, 204, 219, 237, 254, 274, 292, 314, 334, 358, 380, 406, 430, 458, 484, 514, 542, 575, 605, 640, 673, 710, 745, 785, 822, 865, 905

Offset

0,3

Comments

a(n) is equal to the number of partitions mu of n+6 of length 4 such that the transpose of mu has an even number of even entries (see below example). - John M. Campbell, Feb 02 2016

Number of partitions of n into parts 1, 2, 3, and 8. - Michel Marcus, Feb 03 2016

Number of partitions of n+4 into 4 parts whose smallest part is odd. - Wesley Ivan Hurt, Jan 19 2021

Links

Table of n, a(n) for n=0..57.

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

Example

From John M. Campbell, Feb 02 2016: (Start)
For example, letting n=6, there are a total of a(n)=a(6)=7 partitions mu of n+6=12 of length 4 such that the transpose of mu has an even number of even entries: (8,2,1,1), (6,4,1,1), (6,3,2,1), (6,2,2,2), (4,4,3,1), (4,4,2,2), (4,3,3,2). For example, the transpose of
   oooooo
   oooo
   o
   o
is
   oooo
   oo
   oo
   oo
   o
   o
and contains 4 even entries. (End)

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^8)), {x, 0, 200}], x] (* John M. Campbell, Feb 02 2016 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^8)) + O(x^80)) \\ Michel Marcus, Feb 03 2016

Crossrefs

Sequence in context: A280083 A020902 A008751 * A280241 A031121 A080655

Adjacent sequences: A028999 A029000 A029001 * A029003 A029004 A029005

Keyword

nonn

Author

N. J. A. Sloane

Status

approved