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 A285009 Subset sums (see Comments). 5
 9, 17, 28, 42, 59, 79, 102, 128, 157, 189, 224, 262, 303, 347, 394, 444, 497, 553, 612, 674, 739, 807, 878, 952, 1029, 1109, 1192, 1278, 1367, 1459, 1554, 1652, 1753, 1857, 1964, 2074, 2187, 2303, 2422, 2544, 2669, 2797, 2928, 3062, 3199, 3339, 3482, 3628, 3777, 3929, 4084 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS 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. 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 REFERENCES a(4) is mentioned in: Gary Gruber, "The World's 200 Hardest Brain Teasers", Sourcebooks, 2010, p. 55. LINKS Colin Barker, Table of n, a(n) for n = 3..1000 Terrel Trotter, Normal Magic Triangles of Order n, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n > 5. a(n) = (8 + (n-2)*(3*n+1))/2, for n > 2. G.f.: x^3*(9 - 10*x + 4*x^2) / (1 - x)^3. - Colin Barker, Apr 08 2017 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 a(n) = A005449(n-1) + 2. - Hugo Pfoertner, Feb 18 2021 EXAMPLE 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. MATHEMATICA Table[(8+(n-2)*(3 *n+1))/2, {n, 3, 53}] Drop[CoefficientList[Series[x^3*(9 - 10*x + 4*x^2) / (1 - x)^3 , {x, 0, 60}], x], 3] (* Indranil Ghosh, Apr 08 2017 *) PROG (PARI) Vec(x^3*(9 - 10*x + 4*x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Apr 08 2017 CROSSREFS Cf. A005449. Sequence in context: A109333 A081030 A352789 * A228260 A147459 A188559 Adjacent sequences: A285006 A285007 A285008 * A285010 A285011 A285012 KEYWORD easy,nonn AUTHOR Ivan N. Ianakiev, Apr 07 2017 STATUS approved

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