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A036011
Number of partitions of n into parts not of the form 25k, 25k+12 or 25k-12. Also number of partitions with at most 11 parts of size 1 and differences between parts at distance 11 are greater than 1.
1
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 132, 171, 223, 285, 367, 464, 590, 740, 930, 1157, 1442, 1780, 2200, 2699, 3311, 4037, 4922, 5967, 7232, 8724, 10516, 12626, 15147, 18104, 21621, 25739, 30610, 36300, 43005, 50815, 59984, 70642
OFFSET
0,3
COMMENTS
Case k=12,i=12 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
LINKS
Eric Weisstein's World of Mathematics, Andrews-Gordon Identity
FORMULA
a(n) ~ exp(2*Pi*sqrt(11*n/3)/5) * 11^(1/4) * cos(Pi/50) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+12-25))*(1 - x^(25*k-12))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A347577 A238869 A326333 * A325856 A104501 A328546
KEYWORD
nonn,easy
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, May 10 2018
STATUS
approved