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Sum of largest parts of all partitions of n into consecutive parts.
3

%I #21 Jul 21 2017 12:11:34

%S 1,2,5,4,8,9,11,8,18,14,17,17,20,19,34,16,26,31,29,26,46,29,35,33,45,

%T 34,58,35,44,58,47,32,70,44,70,57,56,49,82,50,62,78,65,53,114,59,71,

%U 65,84,76,106,62,80,98,106,67,118,74,89,106,92,79,153,64,124

%N Sum of largest parts of all partitions of n into consecutive parts.

%C If n is a power of 2 then a(n) = n, the same as A286014(n).

%C Conjecture: this is also the row sums of A286013.

%H Alois P. Heinz, <a href="/A286015/b286015.txt">Table of n, a(n) for n = 1..10000</a>

%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 sum of the largest parts is 15 + 8 + 6 + 5 = 34, so a(15) = 34.

%t Table[Total[Select[IntegerPartitions@ n, Or[Length@ # == 1, Union@ Differences@ # == {-1}] &][[All, 1]]], {n, 65}] (* _Michael De Vlieger_, Jul 21 2017 *)

%Y Cf. A000079, A006128, A046746, A204217, A211343, A245579, A286013, A286014.

%K nonn

%O 1,2

%A _Omar E. Pol_, Apr 30 2017

%E More terms from _Alois P. Heinz_, May 01 2017