A286014 Sum of smallest parts of all partitions of n into consecutive parts.

1, 2, 4, 4, 7, 7, 10, 8, 15, 11, 16, 15, 19, 16, 27, 16, 25, 26, 28, 22, 38, 26, 34, 31, 40, 31, 50, 29, 43, 49, 46, 32, 62, 41, 59, 48, 55, 46, 74, 46, 61, 67, 64, 46, 94, 56, 70, 63, 77, 69, 98, 55, 79, 85, 92, 61, 110, 71, 88, 93, 91, 76, 131, 64, 110, 103

Offset

1,2

Comments

If n is a power of 2 then a(n) = n, the same as A286015(n).

Conjecture: this is also the row sums of A211343.

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 smallest parts is 15 + 7 + 4 + 1 = 27, so a(15) = 27.

Mathematica

Table[Total[Select[IntegerPartitions@ n, Or[Length@ # == 1, Union@ Differences@ # == {-1}] &][[All, -1]]], {n, 66}] (* Michael De Vlieger, Jul 21 2017 *)

Crossrefs

Cf. A000079, A046746, A204217, A211343, A245579, A286015.

Sequence in context: A233272 A023844 A132083 * A102465 A139825 A347067

Adjacent sequences: A286011 A286012 A286013 * A286015 A286016 A286017

Keyword

nonn

Author

Omar E. Pol, Apr 30 2017

Extensions

More terms from Alois P. Heinz, May 01 2017

Status

approved