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A035981
Number of partitions in parts not of the form 21k, 21k+3 or 21k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 9 are greater than 1.
0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 208, 258, 328, 404, 507, 621, 772, 941, 1159, 1406, 1719, 2075, 2520, 3028, 3656, 4374, 5252, 6259, 7479, 8879, 10561, 12493, 14800, 17448, 20590, 24196, 28453, 33335, 39069, 45641
OFFSET
1,2
COMMENTS
Case k=10,i=3 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(Pi/7) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 3-21))*(1 - x^(21*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035957 A035964 A035972 * A035991 A036002 A104504
KEYWORD
nonn,easy
STATUS
approved