|
|
A213423
|
|
Number of partitions of n in which all parts are >= 2 and the largest part occurs at least four times.
|
|
1
|
|
|
1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 4, 2, 6, 3, 7, 5, 11, 7, 13, 11, 19, 15, 25, 21, 34, 30, 44, 42, 60, 56, 78, 78, 105, 103, 137, 139, 181, 186, 234, 246, 309, 323, 399, 425, 519, 554, 670, 721, 864, 934, 1108, 1206, 1425, 1548, 1816, 1989, 2318, 2539, 2945, 3235, 3738, 4111, 4726
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
8,5
|
|
LINKS
|
|
|
FORMULA
|
a(n) = p(n)-2*p(n-1)+p(n-3)+p(n-4)-2*p(n-6)+p(n-7), where p(n) = A000041(n).
G.f.: (1-x)*Product_{k>3} 1/(1-x^k).
a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^4 / (24*sqrt(3)*n^3). - Vaclav Kotesovec, Jun 02 2018
|
|
EXAMPLE
|
For n = 16 we have three partitions: {[4+4+4+4], [3+3+3+3+2+2], [2+2+2+2+2+2+2+2]}, so a(16) = 3.
|
|
MAPLE
|
seq(combinat:-numbpart(n)-2*combinat:-numbpart(n-1)+combinat:-numbpart(n-3)+combinat:-numbpart(n-4)-2*combinat:-numbpart(n-6)+combinat:-numbpart(n-7), n=8..70)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|