login
A035963
Number of partitions of n into parts not of the form 17k, 17k+2 or 17k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 7 are greater than 1.
0
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 74, 95, 119, 151, 188, 235, 292, 361, 443, 546, 666, 812, 986, 1196, 1442, 1740, 2088, 2504, 2993, 3572, 4248, 5051, 5983, 7080, 8358, 9855, 11589, 13618, 15962, 18691, 21844, 25499, 29708, 34583, 40181
OFFSET
1,3
COMMENTS
Case k=8,i=2 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * sin(2*Pi/17) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 2-17))*(1 - x^(17*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A208856 A105782 A035956 * A035971 A035980 A035990
KEYWORD
nonn,easy
STATUS
approved