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A035980
Number of partitions of n into parts not of the form 21k, 21k+2 or 21k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 9 are greater than 1.
0
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 192, 241, 300, 372, 458, 566, 693, 847, 1032, 1255, 1518, 1837, 2211, 2659, 3188, 3815, 4551, 5426, 6446, 7649, 9056, 10707, 12627, 14878, 17488, 20533, 24064, 28165, 32904, 38405
OFFSET
1,3
COMMENTS
Case k=10,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(n/7)) * sin(2*Pi/21) / (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+ 2-21))*(1 - x^(21*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035956 A035963 A035971 * A035990 A036001 A027336
KEYWORD
nonn,easy
STATUS
approved