A036020 Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 16k-1.

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

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, Addison-Wesley, 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][(k-1)%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