

A036027


Number of partitions of n into parts not of form 4k+2, 20k, 20k+7 or 20k7. Also number of partitions in which no odd part is repeated, with at most 3 parts of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.


0



1, 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 24, 29, 35, 44, 55, 67, 80, 97, 119, 143, 168, 201, 243, 287, 336, 398, 471, 552, 643, 751, 881, 1025, 1184, 1374, 1597, 1842, 2117, 2440, 2812, 3226, 3689, 4223, 4837, 5520, 6280, 7152, 8148, 9251, 10481, 11883, 13466
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OFFSET

1,3


COMMENTS

Case k=5,i=4 of Gordon/Goellnitz/Andrews Theorem.


REFERENCES

G. E. Andrews, The Theory of Partitions, AddisonWesley, 1976, p. 114.


LINKS

Table of n, a(n) for n=1..52.


FORMULA

a(n) ~ exp(Pi*sqrt(2*n/5)) * cos(3*Pi/20) / (10^(3/4) * n^(3/4)).  Vaclav Kotesovec, May 10 2018


MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1  x^(4*k  2))*(1  x^(20*k))*(1  x^(20*k+720))*(1  x^(20*k 7))/(1  x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)


CROSSREFS

Sequence in context: A331016 A125155 A091179 * A036032 A008813 A133463
Adjacent sequences: A036024 A036025 A036026 * A036028 A036029 A036030


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


EXTENSIONS

Name corrected by Vaclav Kotesovec, May 09 2018


STATUS

approved



