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%I #18 Jul 04 2020 03:11:21
%S 1,1,1,1,2,2,3,4,6,7,9,11,15,18,23,28,37,44,55,66,83,99,121,145,179,
%T 212,255,303,366,431,514,606,723,847,999,1169,1380,1607,1881,2189,
%U 2561,2967,3449,3990,4633,5342,6172,7105,8201,9412,10816,12394,14225,16257,18596,21220
%N a(n) is the number of partitions of n without repeated odd parts such that the total number of parts congruent to 0,3, or 5 modulo 8 is even.
%H J. Huh and B. Kim, <a href="https://doi.org/10.114/S1793042120500475">The number of equivalence classes arising from partition involutions</a>, Int. J. Number Theory, 16 (2020), 925-939.
%F G.f.: 1/2*(Product_{n>=1} (1-q^(2*n-1))/(1-q^(2*n)) + Product_{n>=1} (1+q^(8*n-7))*(1-q^(8*n-5))*(1-q^(8*n-3))*(1+q^(8*n-1))/((1-q^(8*n-6))*(1-q^(8*n-4))*(1-q^(8*n-2))*(1+q^(8*n)))).
%e a(8) = 6, the relevant partitions of 8 without repeated odd parts being [7,1], [6,2], [5,3], [4,4], [4,2,2], [2,2,2,2].
%Y Cf. A006950.
%K nonn
%O 0,5
%A _Jeremy Lovejoy_, Jul 02 2020
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