A035941 Number of partitions of n into parts not of the form 9k, 9k+2 or 9k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 3 are greater than 1.

1, 1, 2, 3, 4, 6, 7, 10, 13, 17, 21, 28, 35, 44, 55, 69, 84, 105, 127, 156, 189, 229, 275, 333, 397, 475, 565, 673, 795, 943, 1109, 1307, 1533, 1798, 2099, 2455, 2855, 3323, 3855, 4472, 5169, 5978, 6890, 7942, 9132, 10495, 12032, 13796, 15778, 18040

Offset

1,3

Comments

Case k=4, i=2 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) ~ sin(2*Pi/9) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 12 2015

Maple

# See A035937 for GordonsTheorem
A035941_list := n -> GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], n):
A035941_list(40); # Peter Luschny, Jan 22 2012

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-3)) * (1 - x^(9*k-4)) * (1 - x^(9*k-5)) * (1 - x^(9*k-6)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 12 2015 *)

Prog

(Sage) # See A035937 for GordonsTheorem
def A035941_list(len) :  return GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], len)
A035941_list(40) # Peter Luschny, Jan 22 2012

Crossrefs

Sequence in context: A181436 A378615 A199118 * A039854 A237752 A032480

Adjacent sequences: A035938 A035939 A035940 * A035942 A035943 A035944

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved