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A035972
Number of partitions in parts not of the form 19k, 19k+3 or 19k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 8 are greater than 1.
0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 129, 161, 207, 256, 325, 400, 501, 613, 761, 927, 1140, 1381, 1686, 2033, 2466, 2959, 3568, 4264, 5113, 6086, 7263, 8612, 10231, 12088, 14302, 16841, 19850, 23298, 27364, 32022, 37485, 43739
OFFSET
1,2
COMMENTS
Case k=9,i=3 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * sin(3*Pi/19) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 3-19))*(1 - x^(19*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035951 A035957 A035964 * A035981 A035991 A036002
KEYWORD
nonn,easy
STATUS
approved