|
|
A035951
|
|
Number of partitions in parts not of the form 13k, 13k+3 or 13k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 5 are greater than 1.
|
|
5
|
|
|
1, 2, 2, 4, 5, 8, 10, 15, 19, 26, 33, 45, 56, 74, 92, 119, 147, 187, 230, 289, 353, 438, 532, 655, 791, 965, 1160, 1405, 1681, 2023, 2409, 2883, 3420, 4070, 4809, 5698, 6707, 7911, 9281, 10904, 12750, 14925, 17397, 20296, 23590, 27431, 31795, 36864
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Case k=6,i=3 of Gordon Theorem.
|
|
REFERENCES
|
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ sin(3*Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 22 2015
|
|
MATHEMATICA
|
nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (1 - x^(13*k-11)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|