|
| |
|
|
A116634
|
|
Number of partitions of n having exactly one part that is a multiple of 3.
|
|
1
| |
|
|
0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 14, 20, 26, 36, 47, 62, 80, 104, 132, 169, 212, 267, 332, 414, 510, 629, 769, 941, 1142, 1386, 1672, 2016, 2417, 2897, 3455, 4118, 4888, 5796, 6849, 8085, 9513, 11182, 13107, 15347, 17923, 20910, 24338, 28298, 32833, 38054, 44021
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
COMMENTS
| Column 1 of A116633.
|
|
|
FORMULA
| G.f.=x^3/[(1-x^3)product((1-x^(3j-2))(1-x^(3j-1)), j=1..infinity)].
|
|
|
EXAMPLE
| a(7)=5 because we have [6,1],[4,3],[3,2,2],[3,2,1,1] and [3,1,1,1,1].
|
|
|
MAPLE
| g:=x^3/(1-x^3)/product((1-x^(3*j-2))*(1-x^(3*j-1)), j=1..30): gser:=series(g, x=0, 56): seq(coeff(gser, x, n), n=0..53);
|
|
|
CROSSREFS
| Cf. A116633, A000726.
Sequence in context: A001522 A054405 A155167 * A035960 A023893 A065094
Adjacent sequences: A116631 A116632 A116633 * A116635 A116636 A116637
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 19 2006
|
| |
|
|
