

A286015


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


3



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, 34, 58, 35, 44, 58, 47, 32, 70, 44, 70, 57, 56, 49, 82, 50, 62, 78, 65, 53, 114, 59, 71, 65, 84, 76, 106, 62, 80, 98, 106, 67, 118, 74, 89, 106, 92, 79, 153, 64, 124
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OFFSET

1,2


COMMENTS

If n is a power of 2 then a(n) = n, the same as A286014(n).
Conjecture: this is also the row sums of A286013.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A000079, A006128, A046746, A204217, A211343, A245579, A286013, A286014.
Sequence in context: A134079 A033686 A243973 * A183542 A080031 A198193
Adjacent sequences: A286012 A286013 A286014 * A286016 A286017 A286018


KEYWORD

nonn


AUTHOR

Omar E. Pol, Apr 30 2017


EXTENSIONS

More terms from Alois P. Heinz, May 01 2017


STATUS

approved



