|
|
A029012
|
|
Expansion of 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).
|
|
0
|
|
|
1, 1, 2, 2, 3, 4, 5, 7, 8, 10, 12, 14, 17, 19, 23, 26, 30, 34, 38, 43, 48, 54, 60, 66, 73, 80, 88, 96, 105, 114, 124, 134, 145, 156, 168, 181, 194, 208, 222, 237, 253, 269, 287, 304, 323, 342, 362, 383, 404, 427, 450
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of partitions of n into parts 1, 2, 5, and 7. - Joerg Arndt, Oct 15 2014
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,-1,0,0,-1,1,0,-1,1,1,-1).
|
|
FORMULA
|
G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).
a(n) = floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16). - Tani Akinari, Oct 15 2014
|
|
MATHEMATICA
|
CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^7)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2014 *)
|
|
PROG
|
(Magma) [Floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16): n in [0..60]]; // Vincenzo Librandi, Oct 15 2014
(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)) + O(x^80)) \\ Michel Marcus, Oct 15 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|