A342713 Partition the integers from 1 to n into three groups with consecutive numbers, then a(n) is the maximum value of the sum of the numbers in the second group multiplied by the minimum of the sum of the numbers in the first and third groups.
2, 9, 21, 54, 90, 144, 234, 350, 504, 714, 950, 1350, 1764, 2156, 2772, 3500, 4374, 5390, 6380, 7812, 9504, 10890, 12740, 14850, 17442, 20475, 23100, 26334, 30444, 34320, 38709, 43146, 48510, 55250, 61047, 66780, 74925, 83600, 92169, 100485, 109350, 121512, 133331, 144000, 156195, 171171
Offset: 3
Keywords
Examples
a(3) = 2 as the only partition is {1},{2},{3}. The minimum sum of the first and third group is 1, thus a(3) = 2*1 = 2.
a(5) = 21 as the three group partition {1,2},{3,4},{5} has a minimum sum of the first and third groups of 1+2 = 3, thus a(5) = 3*(3+4) = 3*7 = 21.
a(12) = 714 as the three group partition {1,2,3,4,5,6},{7,8,9,10},{11,12} has a minimum sum of the first and third groups of 1+2+3+4+5+6 = 21, thus a(12) = 21*(7+8+9+10) = 21*34 = 714.
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