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%I #31 May 24 2018 09:04:42
%S 1,1,1,1,1,1,1,2,2,2,3,3,3,4,5,5,5,6,6,7,9,10,11,12,13,14,16,18,19,21,
%T 23,25,28,31,34,37,40,43,47,52,56,61,66,71,78,85,92,99,107,115,124,
%U 135,145,156,168,180,194,210,226,242,260,278,297,320,343,367,393,420,449,481,516,550,587,626,666,712,760,810,863,919,978,1041,1110,1180,1254,1333,1414,1503,1598,1697,1801
%N Number of partitions of n into distinct parts congruent to 1, 2, or 4 modulo 6.
%C a(n) is also the number of partitions of n into parts congruent to 1, 7, or 10 modulo 12.
%C a(n) is also the number of partitions of n into parts that differ by at least 6, where the inequality is strict if the larger part is 0, 3, or 5 modulo 6, with the exception that 6+1 may appear.
%H Robert Israel, <a href="/A253144/b253144.txt">Table of n, a(n) for n = 0..10000</a>
%H K. Alladi and G. E. Andrews, <a href="http://dx.doi.org/10.1007/s11139-014-9617-0">The dual of Göllnitz's (big) partition theorem</a>, Ramanujan J. 36 (2015), 171-201.
%F a(n) ~ exp(sqrt(n/6)*Pi) / (2^(17/12) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, May 24 2018
%e a(14) = 5, the valid partitions being 14, 13+1, 10+4, 8+4+2, and 7+4+2+1.
%p series(mul((1+x^(6*k+1))*(1+x^(6*k+2))*(1+x^(6*k+4)),k=0..100),x=0,100)
%Y Cf. A056970.
%K nonn
%O 0,8
%A _Jeremy Lovejoy_, Mar 23 2015
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