

A036024


Number of partitions of n into parts not of form 4k+2, 20k, 20k+1 or 20k1. Also number of partitions in which no odd part is repeated, with no part 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



0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 7, 8, 12, 15, 16, 19, 24, 30, 34, 39, 49, 60, 67, 77, 95, 112, 127, 147, 175, 206, 234, 267, 315, 367, 415, 474, 553, 637, 720, 820, 945, 1082, 1223, 1384, 1585, 1807, 2032, 2294, 2612, 2957, 3321, 3738, 4229, 4770, 5344
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OFFSET

1,7


COMMENTS

Case k=5,i=1 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..57.


FORMULA

a(n) ~ exp(Pi*sqrt(2*n/5)) * sin(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+120))*(1  x^(20*k 1))/(1  x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)


CROSSREFS

Sequence in context: A260460 A000025 A036020 * A036029 A181530 A035362
Adjacent sequences: A036021 A036022 A036023 * A036025 A036026 A036027


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



