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A237751 Number of partitions of n such that 2*(greatest part) < (number of parts). 9

%I #11 Jan 24 2022 04:40:21

%S 0,0,1,1,1,2,3,4,6,8,10,14,18,24,32,41,52,67,85,107,135,169,210,263,

%T 324,400,493,604,736,899,1091,1322,1599,1929,2319,2787,3336,3989,4760,

%U 5669,6734,7994,9465,11192,13211,15571,18319,21531,25257,29594,34626

%N Number of partitions of n such that 2*(greatest part) < (number of parts).

%C Also, the number of partitions of n such that (greatest part) > 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) < 0.

%H Seiichi Manyama, <a href="/A237751/b237751.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000041(n) - A237755(n).

%e a(6) = 2 counts these partitions: 21111, 111111.

%t z = 55; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] < Length[p]], {n, z}]

%Y Cf. A064173, A237752-A237757, A000041.

%K nonn,easy

%O 1,6

%A _Clark Kimberling_, Feb 13 2014

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)