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%I #19 May 17 2023 08:34:42
%S 1,0,0,0,1,1,2,3,5,6,9,11,16,20,27,33,45,55,72,89,116,142,181,222,281,
%T 343,429,522,649,786,967,1168,1429,1719,2088,2504,3026,3615,4345,5174,
%U 6192,7349,8755,10360,12297,14507,17154,20182,23788,27910,32790,38374,44955,52480,61307,71402
%N Number of partitions p of n such that (1/3)*max(p) is a part of p.
%H Seiichi Manyama, <a href="/A363066/b363066.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..3*k} (1-x^j).
%e a(7) = 3 counts these partitions: 331, 3211, 31111.
%o (PARI) a(n) = sum(k=0, n\4, #partitions(n-4*k, 3*k));
%Y Cf. A002865, A238479, A363067, A363068.
%Y Cf. A008484, A237825, A363045.
%K nonn
%O 0,7
%A _Seiichi Manyama_, May 16 2023
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