A035980 - OEIS

A035980

Number of partitions of n into parts not of the form 21k, 21k+2 or 21k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 9 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 121, 154, 192, 241, 300, 372, 458, 566, 693, 847, 1032, 1255, 1518, 1837, 2211, 2659, 3188, 3815, 4551, 5426, 6446, 7649, 9056, 10707, 12627, 14878, 17488, 20533, 24064, 28165, 32904, 38405

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OFFSET

1,3

COMMENTS

Case k=10,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..48.

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(2*Pi/21) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 2-21))*(1 - x^(21*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035956 A035963 A035971 * A035990 A036001 A027336

Adjacent sequences: A035977 A035978 A035979 * A035981 A035982 A035983

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved