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A035947
Number of partitions of n into parts not of the form 11k, 11k+4 or 11k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 4 are greater than 1.
0
1, 2, 3, 4, 6, 9, 11, 16, 21, 28, 36, 48, 60, 78, 98, 124, 154, 194, 238, 296, 362, 444, 539, 658, 793, 960, 1152, 1384, 1652, 1976, 2345, 2789, 3299, 3902, 4596, 5416, 6352, 7454, 8715, 10186, 11869, 13828, 16059, 18648, 21598, 25000, 28873, 33332
OFFSET
1,2
COMMENTS
Case k=5,i=4 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ cos(3*Pi/22) * sqrt(2) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 21 2015
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)
CROSSREFS
Sequence in context: A130899 A007210 A198394 * A371839 A338914 A048249
KEYWORD
nonn,easy
STATUS
approved