|
|
A036000
|
|
Number of partitions in parts not of the form 25k, 25k+1 or 25k-1. Also number of partitions with no part of size 1 and differences between parts at distance 11 are greater than 1.
|
|
1
|
|
|
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 319, 382, 476, 572, 704, 842, 1031, 1228, 1492, 1775, 2140, 2539, 3047, 3601, 4299, 5071, 6023, 7083, 8382, 9828, 11584, 13552, 15912, 18568, 21736, 25296, 29520
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
Case k=12,i=1 of Gordon Theorem.
|
|
REFERENCES
|
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * sin(Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
|
|
MATHEMATICA
|
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 1-25))*(1 - x^(25*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|