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A035978
Number of partitions of n into parts not of the form 19k, 19k+9 or 19k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 8 are greater than 1.
1
1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 53, 72, 93, 123, 158, 205, 260, 333, 418, 529, 659, 824, 1019, 1264, 1551, 1908, 2328, 2843, 3448, 4185, 5048, 6092, 7313, 8777, 10489, 12531, 14910, 17733, 21019, 24896, 29399, 34692, 40824, 48004, 56307
OFFSET
0,3
COMMENTS
Case k=9,i=9 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
LINKS
FORMULA
a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 09 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[((1 - x^(19*k))*(1 - x^(19*k - 9))*(1 - x^(19*k - 10)))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 09 2018 *)
CROSSREFS
Sequence in context: A008631 A347574 A238866 * A319475 A319454 A023029
KEYWORD
nonn,easy
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, May 08 2018
STATUS
approved