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
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
KEYWORD
nonn
AUTHOR
STATUS
approved