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A363066
Number of partitions p of n such that (1/3)*max(p) is a part of p.
4
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, 343, 429, 522, 649, 786, 967, 1168, 1429, 1719, 2088, 2504, 3026, 3615, 4345, 5174, 6192, 7349, 8755, 10360, 12297, 14507, 17154, 20182, 23788, 27910, 32790, 38374, 44955, 52480, 61307, 71402
OFFSET
0,7
LINKS
FORMULA
G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..3*k} (1-x^j).
EXAMPLE
a(7) = 3 counts these partitions: 331, 3211, 31111.
PROG
(PARI) a(n) = sum(k=0, n\4, #partitions(n-4*k, 3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 16 2023
STATUS
approved