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Total number of parts in all partitions of all positive integers <= n into consecutive parts.
7

%I #50 Nov 07 2019 13:25:33

%S 1,2,5,6,9,13,16,17,23,28,31,35,38,43,54,55,58,66,69,75,87,92,95,99,

%T 107,112,124,132,135,148,151,152,164,169,184,196,199,204,216,222,225,

%U 240,243,252,278,283,286,290,300,310,322,331,334,351,369,377,389,394,397,414,417,422,450,451,469,488,491,500,512,529

%N Total number of parts in all partitions of all positive integers <= n into consecutive parts.

%C Partial sums of A204217.

%C Sum of first n rows of the triangle A285914.

%C Where records occur in A328365. - _Omar E. Pol_, Oct 22 2019

%C Row sums of A328368. - _Omar E. Pol_, Nov 04 2019

%e For n = 15 there are four partitions of 15 into consecutive parts: [15], [8, 7], [6, 5, 4] and [5, 4, 3, 2, 1]. The total number of parts in these four partitions is 11, and a(14) = 43, so a(15) = 43 + 11 = 54.

%Y Cf. A001227, A196020, A204217, A235791, A237048, A237591, A237593, A245092, A285900, A285914, A299765, A328361, A328362, A328365, A328368.

%K nonn

%O 1,2

%A _Omar E. Pol_, May 02 2017