A036022 Number of partitions of n into parts not of form 4k+2, 16k, 16k+5 or 16k-5.

1, 1, 1, 2, 3, 3, 4, 6, 8, 10, 12, 15, 20, 24, 28, 36, 45, 53, 63, 77, 93, 110, 129, 154, 185, 216, 251, 297, 350, 405, 469, 548, 638, 736, 846, 978, 1131, 1295, 1480, 1701, 1951, 2222, 2529, 2886, 3288, 3730, 4224, 4793, 5436, 6138, 6921, 7819, 8823, 9922, 11150

Offset

0,4

Comments

Case k=4,i=3 of Gordon/Goellnitz/Andrews Theorem.

Also number of partitions in which no odd part is repeated, with at most 2 parts 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 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,...]. - 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..54.

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-([1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0][(k-1)%16+1])*x^k, 1+x*O(x^n)), n))

Crossrefs

Sequence in context: A036021 A036025 A036030 * A036026 A116494 A036031

Adjacent sequences: A036019 A036020 A036021 * A036023 A036024 A036025

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved