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A036004
Number of partitions of n into parts not of the form 25k, 25k+5 or 25k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 11 are greater than 1.
0
1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 134, 175, 220, 284, 355, 450, 560, 703, 867, 1080, 1324, 1633, 1993, 2441, 2960, 3604, 4350, 5262, 6324, 7610, 9104, 10905, 12993, 15490, 18390, 21835, 25825, 30550, 36013, 42445, 49880, 58595
OFFSET
1,2
COMMENTS
Case k=12,i=5 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * ((11*(3 - sqrt(5)))/30)^(1/4) / (10 * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 5-25))*(1 - x^(25*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035974 A035983 A035993 * A027339 A039837 A039838
KEYWORD
nonn,easy
STATUS
approved