login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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