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.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved