A286015 Sum of largest parts of all partitions of n into consecutive parts.

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

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 A328203 A080031

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