OFFSET
0,6
COMMENTS
Number of partitions of n into distinct parts that are not congruent to 3 mod 4 and the number of partitions of n into odd parts such that each part which is congruent to 3 mod 4 occurs an even number of times.
FORMULA
G.f.: prod_{k >= 0} 1/{(1 - x^{8k + 1})(1 - x^{8k + 5})(1 - x^{8k + 6})}.
Euler transform of period 8 sequence [1, 0, 0, 0, 1, 1, 0, 0, ...]. - Michael Somos, Jul 29 2005
PROG
(PARI) {a(n)=if(n< 0, 0, polcoeff( 1/prod(k=1, n, 1-[0, 1, 0, 0, 0, 1, 1, 0][k%8+1]*x^k, 1+x*O(x^n)), n))} /* Michael Somos, Jul 29 2005 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. Sato, Jul 20 2005
STATUS
approved