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 A285009 #24 May 08 2024 02:15:57
%S A285009 9,17,28,42,59,79,102,128,157,189,224,262,303,347,394,444,497,553,612,
%T A285009 674,739,807,878,952,1029,1109,1192,1278,1367,1459,1554,1652,1753,
%U A285009 1857,1964,2074,2187,2303,2422,2544,2669,2797,2928,3062,3199,3339,3482,3628,3777,3929,4084
%N A285009 Subset sums (see Comments).
%C A285009 For n > 2, take the set [3*(n-1)] and form three subsets all of which: a) have cardinality of n, b) have the same sum of elements, and c) share one element with the other subset and another element with the third subset. a(n) is the sum of the elements of each subset.
%C A285009 a(n) is the minimum value of the magic constant in a normal magic triangle of order n (see formula 5 in Trotter). - _Stefano Spezia_, Feb 18 2021
%D A285009 a(4) is mentioned in: Gary Gruber, "The World's 200 Hardest Brain Teasers", Sourcebooks, 2010, p. 55.
%H A285009 Colin Barker, <a href="/A285009/b285009.txt">Table of n, a(n) for n = 3..1000</a>
%H A285009 Terrel Trotter, <a href="https://www.trottermath.net/simpleops/magictri.html">Normal Magic Triangles of Order n</a>, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.
%H A285009 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A285009 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n > 5.
%F A285009 a(n) = (8 + (n-2)*(3*n+1))/2, for n > 2.
%F A285009 G.f.: x^3*(9 - 10*x + 4*x^2) / (1 - x)^3. - _Colin Barker_, Apr 08 2017
%F A285009 E.g.f.: (1/2)*exp(x)*(3*x^2 - 2*x + 6) - 2*x*(x + 1) - 3. - _Indranil Ghosh_, Apr 08 2017; corrected by _Ilya Gutkovskiy_, Apr 10 2017
%F A285009 a(n) = A005449(n-1) + 2. - _Hugo Pfoertner_, Feb 18 2021
%e A285009 For n = 3, the set is S = {1,2,3,4,5,6} and the subsets are S1 = {1,2,6}, S2 = {1,3,5} and S3 = {2,3,4}. Therefore, a(3) = 9.
%t A285009 Table[(8+(n-2)*(3 *n+1))/2,{n,3,53}]
%t A285009 Drop[CoefficientList[Series[x^3*(9 - 10*x + 4*x^2) / (1 - x)^3 , {x, 0, 60}], x], 3] (* _Indranil Ghosh_, Apr 08 2017 *)
%o A285009 (PARI) Vec(x^3*(9 - 10*x + 4*x^2) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, Apr 08 2017
%Y A285009 Cf. A005449.
%K A285009 easy,nonn
%O A285009 3,1
%A A285009 _Ivan N. Ianakiev_, Apr 07 2017