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A036002
Number of partitions in parts not of the form 25k, 25k+3 or 25k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 11 are greater than 1.
0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 209, 259, 330, 407, 511, 627, 781, 953, 1176, 1428, 1749, 2114, 2572, 3095, 3743, 4485, 5394, 6438, 7706, 9162, 10916, 12933, 15346, 18120, 21418, 25208, 29691, 34840, 40898, 47852
OFFSET
1,2
COMMENTS
Case k=12,i=3 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^(1/4) * sin(3*Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 3-25))*(1 - x^(25*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035972 A035981 A035991 * A104504 A027337 A364892
KEYWORD
nonn,easy
STATUS
approved