Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 May 09 2014 02:46:36
%S 1,1,1,1,1,2,3,3,3,4,5,6,7,8,10,12,13,15,18,21,24,27,31,36,41,46,52,
%T 60,68,76,86,97,109,122,136,153,172,191,212,237,264,293,325,360,400,
%U 443,488,539,596,657,723,796,876,963,1057,1159,1272,1395,1526,1669,1827
%N Number of partitions of n into parts that are congruent to 1, 5 or 6 mod 8.
%C 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.
%F G.f.: prod_{k >= 0} 1/{(1 - x^{8k + 1})(1 - x^{8k + 5})(1 - x^{8k + 6})}.
%F Euler transform of period 8 sequence [1, 0, 0, 0, 1, 1, 0, 0, ...]. - _Michael Somos_, Jul 29 2005
%o (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 */
%K nonn
%O 0,6
%A _N. Sato_, Jul 20 2005