This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342713 #10 Mar 24 2021 23:05:45
%S A342713 2,9,21,54,90,144,234,350,504,714,950,1350,1764,2156,2772,3500,4374,
%T A342713 5390,6380,7812,9504,10890,12740,14850,17442,20475,23100,26334,30444,
%U A342713 34320,38709,43146,48510,55250,61047,66780,74925,83600,92169,100485,109350,121512,133331,144000,156195,171171
%N 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.
%C A342713 The maximum product is obtained by making the sum of the numbers in the first and third groups as close as possible to each other and to half the sum of the numbers in the second group.
%C A342713 Geometrically the value of a(n) corresponds to the maximum area surrounded by three sides in a square-bottom 'U' shaped figure where the sides are drawn with single steps of incrementing length from 1 to n.
%e A342713 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.
%e A342713 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.
%e A342713 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.
%Y A342713 Cf. A000217, A006011, A007294, A008443, A286430.
%K A342713 nonn
%O A342713 3,1
%A A342713 _Scott R. Shannon_, Mar 20 2021