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A286014
Sum of smallest parts of all partitions of n into consecutive parts.
3
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 30 2017
EXTENSIONS
More terms from Alois P. Heinz, May 01 2017
STATUS
approved