

A036020


Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 16k1.


0



1, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 7, 8, 11, 14, 15, 18, 23, 28, 32, 36, 45, 55, 61, 70, 86, 101, 114, 131, 155, 182, 206, 234, 275, 319, 359, 408, 474, 544, 612, 694, 797, 909, 1023, 1153, 1315, 1494, 1673, 1881, 2134, 2407, 2693, 3019, 3403, 3825, 4269, 4768
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OFFSET

0,8


COMMENTS

Case k=4,i=1 of Gordon/Goellnitz/Andrews Theorem.
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 3 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even.
Euler transform of period 16 sequence [0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,...].  Michael Somos, Jul 15 2004


REFERENCES

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


LINKS

Table of n, a(n) for n=0..58.


FORMULA

a(n) ~ 3^(1/4) * sqrt(2  sqrt(2 + sqrt(2))) * exp(sqrt(3*n/2)*Pi/2) / (2^(15/4) * n^(3/4)).  Vaclav Kotesovec, May 09 2018


PROG

(PARI) a(n)=if(n<0, 0, polcoeff(1/prod(k=1, n, 1([0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0][(k1)%16+1])*x^k, 1+x*O(x^n)), n))


CROSSREFS

Sequence in context: A060210 A260460 A000025 * A036024 A036029 A181530
Adjacent sequences: A036017 A036018 A036019 * A036021 A036022 A036023


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



